Carl Pomerance

Phone: (603) 646-2635
Dept. Fax: (603) 646-1312
Office: 339 Kemeny Hall
Office Hours: Monday, Wednesday, Friday
9:00 - 9:55 AM 
Email: carl.pomerance@dartmouth.edu
US Mail: Department of Mathematics
Dartmouth College
Hanover, NH 03755-3551
(603) 646-2415

Resumé


Books

  1. Lecture Notes on Primality Testing and Factoring: A Short Course at Kent State University, C. Pomerance, MAA Notes 4, Washington, DC, 1984.

  2. Advances in Cryptology: Crypto '87, C. Pomerance, ed., Lecture Notes in Computer Science 293, Springer–Verlag, Berlin, 1988.

  3. Cryptology and computational number theory, C. Pomerance, ed. Proc. Symp. Appl. Math. 42, Amer. Math. Soc., Providence, 1990.

  4. Prime numbers: a computational perspective, R. E. Crandall and C. Pomerance, Springer–Verlag, New York, 2001.

  5. Prime Numbers: a computational perspective, second edition, R. E. Crandall and C. Pomerance, Springer, New York, 2005. Errata.

  6. Topics in combinatorial number theory: Proceedings of the INTEGERS Conference 2003 in honor of Tom Brown, B. Landman, M. Nathanson, J. Nesetril, and C. Pomerance, eds., DIMATIA, Prague, 2005.

  7. Combinatorial Number Theory: Proceedings of the Integers Conference 2005 in Celebration of the 70th Birthday of Ron Graham, B. Landman, M. Nathanson, J. Nesetril, R. Nowakowski, and C. Pomerance, eds., De Gruyter, Berlin, 2007.


Some Talks

  1. Covering talk, Talk on covering congruences (Joint Math Meetings, San Diego, January 2008).

  2. Undergrad covering talk, More elementary talk on covering congruences (Spuyten Duyvil Undergraduate Mathematics Meeting, New York City, April, 2008; Ohio and Michigan MAA Sections, Spring 2008).

  3. Talk on Euler's function, Talk at University of Georgia, February 2008 and Trinity University, March 2008.

  4. Elementary primality talk, Lucas Lecture at Fibonacci Association Meeting in Patras, Greece, July 2008.

  5. Fields talk, Counting Fields. At Canadian Number Theory Association Meeting in Waterloo, Canada, July 2008. Version for Berkeley Number Theory Seminar, February 2010.
  6. Multiplicative order talk, The multiplicative order mod n, on average. At the Quebec/Maine number theory conference at Laval University, Quebec, Canada, October, 2008.
  7. Order and chaos, At the PANTS meeting (yes, a "long PANTS talk"), University of South Carolina, Columbia, SC, December, 2008. Version of March, 2009, Brigham Young University. Version of April, 2009, University of Rochester.
  8. Sociable numbers: new developments on an ancient problem, Session on the Beauty and Power of Number Theory, Joint Mathematics Meetings, Washington, DC, January, 2009.
    Long version of March, 2009, Brigham Young University undergraduate colloquium.
    Long version of April, 2009, Lorentz Center, Leiden, The Netherlands.
    The first dynamical system? AMS Special Session, Boston College, April, 2013.
  9. A 1935 Erdős paper on prime numbers and Euler's function, at the AMS Central Section meeting, University of Illinois, Urbana, IL, March, 2009.
    Version of July, 2009, at the University of Montreal and at the 41st Conference on Combinatorics, Graph Theory and Computing, Version of December, 2009, at the West Coast Number Theory Conference.
  10. Discrete Logarithms, Dartmouth Number Theory Seminar, November 19, 2009.
  11. Fixed points for discrete logarithms, 41st Conference on Combinatorics, Graph Theory, and Computing, Boca Raton, FL, March 2010.
    Related talk: The Pólya–Vinogradov inequality, Illinois Number Theory Conference in Honor of Harold Diamond, May 21, 2010.
    Related talk: Fixed points for discrete logarithms, ANTS IX, Nancy, France, July 19–23, 2010.

  12. Fibonacci integers, Banff conference in honor of Cam Stewart, May 31, 2010 to June 4, 2010.

  13. Counting in number theory, the Rademacher Lectures, U Penn, September, 2010:
    Elementary number theory,
    Finite cyclic groups,
    Fibonacci integers,
    Counting fields

  14. Two problems in combinatorial number theory,
    Number theory and its applications, Debrecen, Hungary, Oct. 4–8, 2010.

  15. Elliptic curves: applications and problems,
    IMA Abel Conference, Minneapolis, MN, January, 2011.

  16. Order and chaos,
    MSRI Arithmetic Statistics Introductory Workshop, Berkeley, CA, January/February, 2011.
    Undergrad version: Order and chaos,
    Hudson River Undergraduate Mathematics Conference, Skidmore College, Saratoga Springs, NY, April 16, 2011.
    Grad version: Order and chaos,
    Quebec Student Conference, University of Montreal, May 20, 2011.
    Short version: A problem of Arnold on the average multiplicative order,
    Maine/Quebec Number Theory Conference, University of Maine, October 1,2, 2011.
    Version of November, 2012
    Version of December, 2013

  17. Product-free sets of integers,
    Integers Conference, Carrollton, GA, October, 2011.
    Sums and products,
    Mathematics & Statistics Colloquium, U. Vermont, December 2, 2011.
    Boston Meetings version,
    Joint Mathematics Meetings, Boston, MA, 2012.
    UC Irvine colloquium, February 9, 2012.
    Sums and products International Number Theory Conference in memory of Alf van der Poorten, AM, March 15, 2012.
    Sums and products Dartmouth Mathematics Society, May 16, 2012.
    Sums and products U. Georgia VIGRE seminar, November 28, 2012.
    Sums and products, West Chester U., April 24, 2013, SUNY Albany, April 25, 2013.
    Sums and products, Arizona State U., February 27, 2014.
    Sums and products, Providence College, April 2, 2014.
    What we still don't know about addition and multiplication, Johns Hopkins Center for Talented Youth, May 4, 2013.
    What we still don't know about addition and multiplication, Richard and Louise Guy Lecture, University of Calgary, September 12, 2013.
    What we still don't know about addition and multiplication, Woods Lecture Series, Butler University, December 3, 2013.
    What we still don't know about addition and multiplication, Fuzzy Vance Lecture, Oberlin College, March 20, 2014.
    What we still don't know about addition and multiplication, Christie Lecture, Bowdoin College, April 7, 2014.

  18. Sets of monotonicity for Euler's function,
    West Coast Number Theory Conference, Asilomar Conference Center, Pacific Grove, CA, December, 2011.

  19. The range of Carmichael's function,
    AMS Sectional Meeting, U. Hawaii, Honolulu, March, 2012.

  20. Balanced subgroups of the multiplicative group,
    Dartmouth Number Theory Seminar, April 26, 2012.
    Balanced subgroups of the multiplicative group,
    CNTA, June, 2012.
    Balanced subgroups of the multiplicative group,
    Quebec/Maine Number Theory Conference, September, 2012.
    Balanced subgroups of the multiplicative group,
    Central Section AMS Meeting, U. Akron, Akron, OH, October, 2012.
    Balanced subgroups of the multiplicative group,
    Palmetto Number Theory Symposium, December 2, 2012.

  21. Some statistical problems concerning the arithmetic functions σ and φ,
    Joint Mathematics Meetings, Special Session on Arithmetic Statistics, San Diego, CA, January, 2013.

  22. Erdős, van der Corput, and the birth of covering congruences,
    Joint Mathematics Meetings, Special Session on Covering Congruences, San Diego, CA, January, 2013.

  23. Paul Erdős and the rise of statistical thinking in elementary number theory,
    Erdős Centennial Conference, Budapest, July 1–5, 2013.
    Paul Erdős and the rise of statistical thinking in elementary number theory,
    Version of 1/15/14 at the Joint Math Meetings, Baltimore.

  24. The set of values of an arithmetic function,
    Mathematical Congress of the Americas, Guanajuato, Mexico, August 9, 2013.
    The set of values of an arithmetic function,
    Integers Conference (marking the Erdős centennial), University of West Georgia, Carrollton, GA, October 23–27, 2013.
    The ranges of various familiar functions,
    CNTA XIII, Carleton University, Ottawa, Canada, June 20, 2014.

  25. Square values of Euler's function,
    SCHOLAR conference in honour of M. Ram Murty, University of Montreal, October 15–17, 2013.

  26. Amicable numbers,
    Illinois Conference in Memory of Felice and Paul Bateman and Heini Halberstam, June 5-7, 2014.

  27. The statistics of elementary number theory,
    2014 NCTS Conference on the Impact of Computation in Number Theory, 30 July, 2014 to 3 August, 2014, National Tsing Hua University, Hsinchu, Taiwan.


Papers

  1. Odd perfect numbers are divisible by at least seven distinct primes, C. Pomerance, Acta Arith. 25 (1974), 265–300.

  2. On Carmichael's conjecture, C. Pomerance, Proc. Amer. Math. Soc. 43 (1974), 297–298.

  3. A search for elliptic curves with large rank, D.E. Penney and C. Pomerance, Math. Comp. 28 (1974), 851–853.

  4. 714 and 715, C. Nelson, D.E. Penney, and C. Pomerance, J. Rec. Math. 7 (1974), 87–89.

  5. Three elliptic curves with rank at least seven, D.E. Penney and C. Pomerance, Math. Comp. 29 (1975), 965–967.

  6. The second largest prime factor of an odd perfect number, C. Pomerance, Math. Comp. 29 (1975), 914–921.

  7. On the congruences σ(n ) ≡ a (mod n ) and na (mod φ(n )), C. Pomerance, Acta Arith. 26 (1975), 265–272.

  8. On an interesting property of 112359550561797752809, J.L. Hunsucker and C. Pomerance, Fibonacci Quarterly 13 (1975), 331–333.

  9. There are no odd super perfect numbers less than 7 x 1024, J.L. Hunsucker and C. Pomerance, Indian J. Math. 17 (1975), 107–120.

  10. Some new results on odd perfect numbers, G.G. Dandapat, J.L. Hunsucker, and C. Pomerance, Pacific J. Math. 57 (1975), 359–364.

  11. On multiply perfect numbers with a special property, C. Pomerance, Pacific J. Math. 57 (1975), 511–517.

  12. On composite n for which φ(n )|n –1, I, C. Pomerance, Acta Arith. 28 (1976), 387–389.

  13. Multiply perfect numbers, Mersenne primes and effective computability, C. Pomerance, Math. Ann. 226 (1977), 195–206.

  14. On a tiling problem of R. B. Eggleton, C. Pomerance, Discrete Math. 18 (1977), 63–70.

  15. On composite n for which φ(n )|n –1, II, C. Pomerance, Pacific J. Math. 69 (1977), 177–186.

  16. On the distribution of amicable numbers, C. Pomerance, J. reine angew. Math. 293/294 (1977), 217–222.

  17. On the largest prime factors of n and n +1, P. Erdős and C. Pomerance, Aequationes Math. 17 (1978), 311–321.

  18. On a class of relatively prime sequences, P. Erdős, D.E. Penney, and C. Pomerance, J. Number Theory 10 (1978), 451–474.

  19. The prime number graph, C. Pomerance, Math. Comp. 33 (1979), 399–408.

  20. On a problem of Evelyn–Linfoot and Page in additive number theory, C. Pomerance and D. Suryanarayana, Publ. Math. Debrecen 26 (1979), 237–244.

  21. Nearly parallel vectors, H.G. Diamond and C. Pomerance, Mathematika 26 (1979), 258–268.

  22. Some number theoretic matching problems, C. Pomerance, Proceedings of the Queen's Number Theory Conference, P. Ribenboim, ed., Queen's Papers in Pure and Applied Mathematics, No. 54, Kingston, Canada, 1979, 237–247.

  23. Collinear subsets of lattice point sequences — an analogue of Szemerédi's theorem, C. Pomerance, J. Combinatorial Theory (A) 28 (1980), 140–149.

  24. A note on the least prime in an arithmetic progression, C. Pomerance, J. Number Theory 12 (1980), 218–223.

  25. The pseudoprimes to 25 x 109, C. Pomerance, J.L. Selfridge, and S.S. Wagstaff, Jr., Math. Comp. 35 (1980), 1003–1026.

  26. Matching the natural numbers up to n with distinct multiples in another interval, P. Erdős and C. Pomerance, Nederl. Akad. Wetensch. Proc. Ser. A 83 (1980), 147–161.

  27. Proof of D.J. Newman's coprime mapping conjecture, C. Pomerance and J.L. Selfridge, Mathematika 27 (1980), 69–83.

  28. Popular values of Euler's function, C. Pomerance, Mathematika 27 (1980), 84–89.

  29. Sets on which an entire function is determined by its range, H.G. Diamond, C. Pomerance, and L. Rubel, Math. Z. 176 (1981), 383–398.

  30. On the distribution of amicable numbers, II, C. Pomerance, J. reine angew. Math. 325 (1981), 183–188.

  31. The arithmetic mean of the divisors of an integer, P.T. Bateman, P. Erdős, C. Pomerance, and E.G. Straus, Analytic Number Theory Proceedings, Philadelphia 1980, M. I. Knopp, ed., Lecture Notes in Math. 899 (1981), 197–220.

  32. On the distribution of pseudoprimes, C. Pomerance, Math. Comp. 37 (1981), 587–593.

  33. Recent developments in primality testing, C. Pomerance, Math. Intelligencer 3 (1981), 97–105.

  34. A new lower bound for the pseudoprime counting function, C. Pomerance, Illinois J. Math. 26 (1982), 4–9.

  35. The search for prime numbers, C. Pomerance, Scientific American 247, No. 6 (1982), 136–144.

  36. Analysis and comparison of some integer factoring algorithms, C. Pomerance, Computational Methods in Number Theory, Part I, H.W. Lenstra, Jr. and R. Tijdeman, eds., Math. Centre Tract 154, Amsterdam, 1982, 89–139.

  37. On distinguishing prime numbers from composite numbers, L.M. Adleman, C. Pomerance, and R.S. Rumely, Annals Math. 117 (1983), 173–206.

  38. An analogue of Grimm's problem of finding distinct prime factors of consecutive integers, P. Erdős and C. Pomerance, Utilitas Math. 24 (1983), 45–65.

  39. On a problem of Oppenheim concerning `Factorisatio Numerorum', E.R. Canfield, P. Erdős, and C. Pomerance, J. Number Theory 17 (1983), 1–28.

  40. Implementation of the continued fraction integer factoring algorithm, C. Pomerance and S.S. Wagstaff, Jr., Congressus Numerantium 37 (1983), 99–117.

  41. On the longest simple path in the divisor graph, C. Pomerance, Proc. Southeastern Conf. Combinatorics, Graph Theory, and Computing, Boca Raton, Florida, 1983, Cong. Num. 40 (1983), 291–304.

  42. Moduli r for which there are many small primes congruent to a modulo r, P.T. Bateman and C. Pomerance, Publ. Math. d'Orsay 83.04 (1983), 8–19.

  43. Lecture notes on primality testing and factoring — A short course at Kent State University, C. Pomerance, (based on notes by S. M. Gagola, Jr.), MAA Notes 4 (1984).

  44. Are there counter-examples to the Baillie—PSW primality test, in DOPO LE PAROLE aangeboden aan DR. A. K. LENSTRA, H. W. Lenstra, jr, J. K. Lenstra, and P. van Emde Boas, eds., Amsterdam, 1984. (Re-typeset by Jon Grantham.)

  45. New ideas for factoring large integers, C. Pomerance, J. W. Smith, and S. S. Wagstaff, Jr., Advances in Cryptology, Proc. Crypto 83, D. Chaum, ed., Plenum Press, New York, 1984, 81–85.

  46. Estimates for certain sums involving the largest prime factor of an integer, A. Ivic and C. Pomerance, Proc. Colloquium on Number Theory 34 (1981), Topics in Classical Number Theory, North Holland, 1984, 769–789.

  47. On the size of the coefficients of the cyclotomic polynomial, P. T. Bateman, C. Pomerance, and R. C. Vaughan, Proc. Colloquium on Number Theory 34 (1981), Topics in Classical Number Theory, North Holland, 1984, 171–202.

  48. View obstruction problems, III, T. W. Cusick and C. Pomerance, J. Number Theory 19 (1984), 131–139.

  49. The normal number of prime factors of φ(n ), P. Erdős and C. Pomerance, Rocky Mtn. J. Math. 15 (1985), 343–352.

  50. On locally repeated values of certain arithmetic functions, I, P. Erdős, C. Pomerance, and A. Sárközy, J. Number Theory 21 (1985), 319–332.

  51. Multiplicative relations for sums of initial k-th powers, D. E. Penney and C. Pomerance, Amer. Math. Monthly 92 (1985), 729–731.

  52. On the distribution of round numbers, C. Pomerance, Number Theory Proceedings, Ootacamund, India 1984, K. Alladi, ed., Lecture Notes in Math. 1122 (1985), 173–200.

  53. The quadratic sieve factoring algorithm, C. Pomerance, Advances in Cryptology, Proceedings of Eurocrypt 84, Paris, 1984, T. Beth. N. Cot, and I. Ingemarsson, eds., Lecture Notes in Computer Sci. 209 (1985), 169–182.

  54. On the Schnirelmann and asymptotic densities of certain sets of non-mulitples, P. Erdős, C. B. Lacampagne, C. Pomerance, and J. L. Selfridge, Proceedings of the Southeast Conference on Combinatorics, Graph Theory, and Computing, Boca Raton, Florida, 1985, Congressus Numerantium 48 (1985), 67–79.

  55. On sums involving reciprocals of the largest prime factor of an integer, P. Erdős, A. Ivic, and C. Pomerance, Glasnik Math. 21 (1986), 283–300.

  56. On the number of false witnesses for a composite number, P. Erdős and C. Pomerance, Math. Comp. 46 (1986), 259–279.

  57. On primitive divisors of Mersenne numbers, C. Pomerance Acta Arith. 46 (1986), 355–367.

  58. On the distribution of the values of Euler's function, C. Pomerance, Acta Arith. 47 (1986), 63–70.

  59. On locally repeated values of certain arithmetic functions, II, P. Erdős, C. Pomerance, and A. Sárközy, Acta Math. Hungarica 49 (1987), 251–259.

  60. On the average number of groups of square-free order, C. Pomerance, Proc. Amer. Math. Soc. 99 (1987), 223–231.

  61. The smallest n-uniform hypergraph with positive discrepancy, N. Alon, D. J. Kleitman, C. Pomerance, M. Saks, and P. Seymour, Combinatorica 7 (1987), 151–160.

  62. On locally repeated values of certain arithmetic functions, III, P. Erdős, C. Pomerance, and A. Sárközy, Proc. Amer. Math. Soc. 101 (1987), 1–7.

  63. Very short primality proofs, C. Pomerance, Math. Comp. 48 (1987), 315–322.

  64. Fast, rigorous factorization and discrete logarithm algorithms, C. Pomerance, Discrete algorithms and complexity, D. S. Johnson, T. Nishizeki, A. Nozaki, H. S. Wilf, eds., Academic Press, Orlando, Florida, 1987, pp. 119–143.

  65. On products of sequences of integers, C. Pomerance and A. Sárközy, Coll. Math. Soc. Janos Bolyai 51 (1987), 447–463.

  66. A pipeline architecture for factoring large integers with the quadratic sieve algorithm, C. Pomerance, J. W. Smith, and R. Tuler, SIAM J. Comput. 17 (1988), 387–403.

  67. On homogeneous multiplicative hybrid problems in number theory, C. Pomerance and A. Sárközy, Acta Arith. 49 (1988), 291–302.

  68. On the number of distinct values of Euler's φ-function, H. Maier and C. Pomerance, Acta Arith. 49 (1988), 263–275.

  69. On divisors of sums of integers, III, C. Pomerance, A. Sárközy, and C. L. Stewart, Pacific J. Math. 133 (1988), 363–379.

  70. The generation of random numbers that are probably prime, P. Beauchemin, G. Brassard, C. Crépeau, C. Goutier, and C. Pomerance, Journal of Cryptology 1 (1988), 53–64.

  71. Two methods in elementary analytic number theory, C. Pomerance, Number theory and applications, R. A. Mollin, ed., Kluwer Academic Publishers, Dordrecht, 1989, pp. 135–161.

  72. On the composition of the arithmetic functions σ and φ, C. Pomerance, Colloq. Math. 58 (1989), 11–15.

  73. The probability that a random probable prime is composite, S.H. Kim and C. Pomerance, Math. Comp. 53 (1989), 721–741.

  74. Fonction zêta de Riemann et conjecture de Weyl–Berry pour les tambours fractals, M. L. Lapidus and C. Pomerance, C. R. Acad. Sci. Paris (Ser. I) 310 (1990), 343–348.

  75. On the normal behavior of the iterates of some arithmetic functions, P. Erdős, A. Granville, C. Pomerance, and C. Spiro, Analytic Number Theory, Proc. Conf. in honor of Paul T. Bateman, B. C. Berndt, et al. eds., Birkhauser, Boston, 1990, pp. 165–204.

  76. Unusually large gaps between consecutive primes, H. Maier and C. Pomerance, Trans. Amer. Math. Soc. 322 (1990), 201–237.

  77. On the least prime in certain arithmetic progressions, A. Granville and C. Pomerance, J. London Math. Soc. (2) 41 (1990), 193–200.

  78. Factoring, C. Pomerance, Cryptology and Computational Number Theory, C. Pomerance, ed., Proc. Symp. Appl. Math. 42, Amer. Math. Soc. Providence, 1990.

  79. Cryptology and computational number theory — an introduction, C. Pomerance, Cryptology and Computational Number Theory, C. Pomerance, ed., Proc. Symp. Appl. Math. 42, Amer. Math. Soc., Providence, 1990.

  80. On a theorem of Besicovitch: values of arithmetic functions that divide their arguments, P. Erdős and C. Pomerance, Indian J. Math. 32 (1990), 279–287.

  81. On the prime divisors of Mersenne numbers, P. Erdős, P. Kiss, and C. Pomerance, Acta Arith. 57 (1991), 267–281.

  82. Carmichael's lambda function, P. Erdős, C. Pomerance, and E. Schmutz, Acta Arith. 58 (1991), 363–385.

  83. The distribution of Lucas and elliptic pseudoprimes, D.M. Gordon and C. Pomerance, Math. Comp. 57 (1991), 825–838.

  84. Grandes déviations pour certaines fonctions arithmétiques, M. Balazard, J.L. Nicolas, C. Pomerance, and G. Tenenbaum, J. Number Theory 40 (1992), 146–164.

  85. The distribution of smooth numbers in arithmetic progressions, A. Balog and C. Pomerance, Proc. Amer. Math. Soc. 115 (1992), 33–43.

  86. A rigorous time bound for factoring integers, H. W. Lenstra, Jr. and C. Pomerance, J. Amer. Math. Soc. 5 (1992), 483–516.

  87. Reduction of huge, sparse matrices over a finite field via created catastrophes, C. Pomerance and J. W. Smith, Experimental Math. 1 (1992), 90–94.

  88. The Riemann zeta function and the one dimensional Weyl-Berry conjecture for fractal drums, M. L. Lapidus and C. Pomerance, Proc. London Math. Soc. (3) 66 (1993), 41–69.

  89. Average case error estimates for the strong probable prime test, I. Damgard, P. Landrock, and C. Pomerance, Math. Comp. 61 (1993), 177–194.

  90. Carmichael numbers, C. Pomerance, Nieuw Arch. Wisk. 11 (1993), 199–209.

  91. On elements of sumsets with many prime factors, P. Erdős, C. Pomerance, A. Sárközy, and C. L. Stewart, J. Number Theory 44 (1993), 93–104.

  92. An upper bound in Goldbach's conjecture, J.M. Deshouillers, A. Granville, W. Narkiewicz, and C. Pomerance, Math. Comp. 61 (1993), 209–213.

  93. Factoring integers with the number field sieve, J. Buhler, H. W. Lenstra, Jr., and C. Pomerance, The development of the number field sieve, A. K. Lenstra and H. W. Lenstra, Jr., eds., Lecture Notes in Math. 1554, pp. 50–94, Springer-Verlag, Berlin, 1993.

  94. A hyperelliptic smoothness test. I, H. W. Lenstra, Jr., J. Pila, and C. Pomerance, Phil. Trans. R. Soc. London A 345 (1993), 397–408.

  95. Sixes and sevens, C. Pomerance, Missouri J. Math. Sci. 6 (1994), 62–63.

  96. There are infinitely many Carmichael numbers, W. R. Alford, A. Granville, and C. Pomerance, Ann. of Math. (2) 139 (1994), 703–722.

  97. On the difficulty of finding reliable witnesses, W. R. Alford, A. Granville, and C. Pomerance, Algorithmic Number Theory Proceedings (ANTS-I), L. M. Adleman and M.-D. Huang, eds., Lecture Notes in Computer Sci. 877 (1994), Springer-Verlag, Berlin, pp. 1–16.

  98. Dickson polynomials with few fixed points in a finite field, C. Pomerance, J. Sichuan U. (Natural Science Ed.) 31 (1994), 460–464.

  99. On a conjecture of R. L. Graham, F. Y. Cheng and C. Pomerance, Rocky Mtn. J. Math. 24 (1994), 961–975.

  100. The number field sieve, C. Pomerance, Mathematics of Computation, 1943–1993, Fifty Years of Computational Mathematics, W. Gautschi, ed., Proc. Symp. Appl. Math. 48, American Mathematical Society, Providence, 1994, pp. 465–480.

  101. Counting the integers factorable via cyclotomic methods, C. Pomerance and J. Sorenson, J. Algorithms, 19 (1995), 250–265.

  102. On a conjecture of Crandall concerning the qx +1 problem, Z. Franco and C. Pomerance, Math. Comp. 64 (1995), 1333–1336.

  103. Implementing the self initializing quadratic sieve on a distributed network, W.R. Alford and C. Pomerance, Number Theoretic and Algebraic Methods in Computer Science, Proc. of Int'l Moscow Conference, June-July, 1993, A. J. van der Poorten, I. Shparlinski, H. G. Zimmer, eds., World Scientific, 1995, pp. 163–174.

  104. Combinatorial number theory, C. Pomerance and A. Sárközy, Handbook of Combinatorics, R. L. Graham, M. Grötschel, L. Lovász, eds., Elsevier Science B.V., 1995, pp. 967–1018.

  105. On the role of smooth numbers in number theoretic algorithms, C. Pomerance, Proceedings of the Intenational Congress of Mathematicians, Zurich, Switzerland 1994, Birkhauser Verlag, Basel, 1995, pp. 411–422.

  106. Counterexamples to the modified Weyl-Berry conjecture, M.L. Lapidus and C. Pomerance, Math. Trans. Cambridge Phil. Soc. 119 (1996), 167–178.

  107. Symmetric and asymmetric primes, P. Fletcher, W. Lindgren, and C. Pomerance, J. Number Theory 58 (1996), 89–99.

  108. Multiplicative independence for random integers, C. Pomerance, Analytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam, Vol. 2, B. Berndt, H. Diamond, A. Hildebrand, eds., Birkhauser, Boston, 1996, pp. 703–711.

  109. On the divisors of n !, P. Erdős, S.W. Graham, A. Ivic, and C. Pomerance, Analytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam, Vol. 1, B. Berndt, H. Diamond, A. Hildebrand, eds., Birkhauser, Boston, 1996, pp. 337–355.

  110. A tale of two sieves, C. Pomerance, The Notices of the Amer. Math. Soc. 43 (1996), 1473–1485.

  111. On primes recognizable in deterministic polynomial time, S. V. Konyagin and C. Pomerance, The mathematics of Paul Erdős, R. L. Graham and J. Nesetril, eds., Springer-Verlag, Berlin, 1997, pp. 176–198.
    See #190 for an update article.

  112. A search for Wieferich and Wilson primes, R. Crandall, K. Dilcher, and C. Pomerance, Math. Comp. 66 (1997), 433–449.

  113. On locally repeated values of certain arithmetic functions, IV, P. Erdős, C. Pomerance, and A. Sárközy, The Ramanujan J. 1 (1997), 227–241.

  114. Automaticity II: Descriptional complexity in the unary case, C. Pomerance, J.M. Robson, and J. Shallit, Theoretical Computer Sci. 180 (1997), 181–201.

  115. Paul Erdős, number theorist extraordinaire, C. Pomerance, The Notices of the Amer. Math. Soc. 45 (1998), 19–23.

  116. Rigorous discrete logarithm computations in finite fields via smooth polynomials, R. Lovorn Bender and C. Pomerance, AMS/IP Studies in Advanced Mathematics 7 (1998), 221–232.

  117. Euler's function in residue classes, T. Dence and C. Pomerance, The Ramanujan Journal 2 (1998), 7–20.

  118. On the distribution of champs, A. Ivic and C. Pomerance, Proceedings of the Fifth Conference of the Canadian Number Theory Association, R. Gupta and K.S. Williams, eds., CRM Proc. 19 (1999), 133–139.

  119. Residue classes free of values of Euler's function, K. Ford, S. V. Konyagin, and C. Pomerance, Number Theory in Progress, K. Gyory, H. Iwaniec, and J. Urbanowicz, eds., vol. 2, de Gruyter, Berlin and New York, 1999, pp. 805–812.

  120. On the solutions to φ(n ) = φ(n +k ), S.W. Graham, J.J. Holt, and C. Pomerance, Number Theory in Progress, K. Gyory, H. Iwaniec, and J. Urbanowicz, eds., vol. 2, de Gruyter, Berlin and New York, 1999, pp. 867–882.

  121. Primes and factorization, J. Grantham and C. Pomerance, Handbook of Discrete Mathematics, K.H. Rosen, ed., CRC Press, 1999.

  122. Small values of the Carmichael function and cryptographic applications, J. Friedlander, C. Pomerance, and I. E. Shparlinski, Proc. Workshop on Cryptography and Computational Number Theory (CCNT'99), K.-Y. Lam, I. E. Shparlinski, H. Wang, and C. Xing, eds., Birkhäuser, 2001, pp. 25–32.

  123. The expected number of random elements to generate a finite abelian group, C. Pomerance, Periodica Mathematica Hungarica 43 (2001), 191–198.

  124. Period of the power generator and small values of the Carmichael function, J. Friedlander, C. Pomerance, and I. E. Shparlinski, Math. Comp., 70 (2001), 1591–1605. Corrigendum, op. cit., 71 (2002), 1803–1806.

  125. Two contradictory conjectures concerning Carmichael numbers, A. Granville and C. Pomerance, Math. Comp., 71 (2001), 883–908.

  126. On the problem of uniqueness for the maximal Stirling number(s) of the second kind, E.R. Canfield and C. Pomerance, Integers, 2 (2002), paper A1, 13 pp.
    (The published form of this paper was somewhat corrupted. The version here also corrects a small error in Section 4. Posted February, 2013.)

  127. On some problems of Makowski–Schinzel and Erdős concerning the arithmetical functions φ and σ, F. Luca and C. Pomerance, Colloq. Math., 92 (2002), 111–130. See also this.

  128. Smooth orders and cryptographic applications, C. Pomerance and I.E. Shparlinski, Proc. ANTS-V, Sydney, Australia, Springer Lecture Notes in Computer Science 2369, (2002), pp. 338–348.

  129. A hyperelliptic smoothness test. II, H. W. Lenstra, Jr., J. Pila, and C. Pomerance, Proc. London Math. Soc., (3) 84 (2002), 105–146.

  130. Ruth–Aaron numbers revisited, C. Pomerance, Paul Erdős and his Mathematics, (Budapest, 1999), Bolyai Soc. Math. Stud. 11, János Bolyai Math. Soc., Budapest, 2002, pp. 567–579.

  131. Primitive roots: a survey, S. Li and C. Pomerance, in New Aspects of Analytic Number Theory (RIMS Kokyuroku No. 1274) (Y. Tanigawa, ed.), and also in Dev. Math. 8, pp. 219–231, Kluwer Academic Publishers, Dordrecht 2002.

  132. On generalizing Artin's conjecture on primitive roots to composite moduli, S. Li and C. Pomerance, J. Reine Angew. Math. 556 (2003), 205–224.

  133. Timed fair exchange of arbitrary signatures, J. A. Garay and C. Pomerance, in Financial Cryptography, 7th International Conference, FC 2003, Lecture Notes in Computer Science 2742, Springer, New York, 2003, pp. 190–207.

  134. Multiplicative structure of values of the Euler function, W. D. Banks, J. B. Friedlander, C. Pomerance, and I. E. Shparlinski, in High Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams (A. Van der Poorten, ed.), Fields Inst. Comm. 41 (2004), pp. 29–47.

  135. Heuristics for class numbers of prime-power real cyclotomic fields, J. Buhler, C. Pomerance, and L. Robertson, in High Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams (A. Van der Poorten, ed.), Fields Inst. Comm. 41 (2004), pp. 149–157.

  136. Prime numbers and the search for extraterrestrial intelligence, C. Pomerance, in Mathematical Adventures for Students and Amateurs, D. Hayes and T. Shubin, eds., M.A.A., 2004, pp. 1–4.

  137. The largest prime factor of a Mersenne number, L. Murata and C. Pomerance, in Number Theory, CNTA Proceedings, Montreal, 2002, CRM Proc. Lecture Notes, 36, Amer. Math. Soc., Providence, RI, 2004, pp. 209–218.

  138. On the binary expansions of algebraic numbers, D. H. Bailey, J. M. Borwein, R. E. Crandall, and C. Pomerance, J. Théorie des Nombres Bordeaux 16 (2004), 487–518.

  139. On the distribution in residue classes of integers with a fixed sum of digits, C. Mauduit, C. Pomerance, and A. Sárközy), Ramanujan J., special issue in honor of J.-L. Nicolas 9 (2005), 45–62.

  140. Products of ratios of consecutive integers, R. de la Bretèche, C. Pomerance, and G. Tenenbaum, Ramanujan J., special issue in honor of J.-L. Nicolas 9 (2005), 131–138.

  141. The iterated Carmichael λ-function and the number of cycles of the power generator, G. Martin and C. Pomerance, Acta Arith. 118 (2005), 305–335.

  142. On the period of the linear congruential and power generators, P. Kurlberg and C. Pomerance, Acta Arith. 119 (2005), 149–169. Extended abstract with title "Lower bounds on the period of some pseudorandom number generators". In Proceedings of Conference on Algorithmic Number Theory 2007, vol. 46 of TUCS Gen. Pub., pages 74–81. Turku Cent. Comput. Sci., Turku, Finland, 2007. .

  143. Finding the group structure of elliptic curves over finite fields, J. B. Friedlander, C. Pomerance, and I. E. Shparlinski, Bull. Austral. Math. Soc. 72 (2005), 251–263.

  144. Primality testing with Gaussian periods, H. W. Lenstra, Jr. and C. Pomerance, preprint from July, 2005. (Revision dated February, 2009.) (Revision dated August, 2009.) (Revision dated October, 2009.) (Revision dated April, 2011.)

  145. On the average number of divisors of the Euler function, F. Luca and C. Pomerance, Publ. Math. Debrecen, 70 (2007), 125–148.

  146. Sieving by large integers and covering systems of congruences, M. Filaseta, K. Ford, S. V. Konyagin, C. Pomerance, and G. Yu, J. Amer. Math. Soc., 20 (2007), 495–517.

  147. Maximal height of divisors of xn  –1, C. Pomerance and N. C. Ryan, Illinois J. Math., 51 (2007), 597–604.

  148. Irreducible radical extensions and Euler-function chains, F. Luca and C. Pomerance, pp. 351–362 in Combinatorial Number Theory, Landman et al., eds., de Gruyter, 2007, and in Integers, 7(2) (2007), paper A25.

  149. Smooth numbers and the quadratic sieve, C. Pomerance, in Algorithmic number theory, J. P. Buhler and P. Stevenhagen, eds., Math. Sci. Res. Inst. Pub. 44, Cambridge U. Press, New York, 2008, pp. 69–81.

  150. Elementary thoughts on discrete logarithms, C. Pomerance, in Algorithmic number theory, J. P. Buhler and P. Stevenhagen, eds., Math. Sci. Res. Inst. Pub. 44, Cambridge U. Press, New York, 2008, pp. 385–396.

  151. Computational number theory, C. Pomerance, in Princeton Companion to Mathematics, W. T. Gowers, ed., Princeton U. Press, Princeton, New Jersey, 2008, pp. 348–362.

  152. On the proportion of numbers coprime to a given integer, P. Erdős, F. Luca, and C. Pomerance, Proceedings of the Anatomy of Integers Conference, Montreal, March 2006, J.-M. De Koninck, A. Granville, F. Luca, eds., CRM Proceedings and Lecture Notes, vol. 46 (2008), 47–64.

  153. Sets with prescribed arithmetic densities, F. Luca, C. Pomerance, and S. Porubsky, Uniform Distribution Theory, 3 (2008), 67–80.

  154. On pseudosquares and pseudopowers, C. Pomerance and I. E. Shparlinski, Combinatorial Number Theory, Proceedings of Integers Conference 2007, de Gruyter, Berlin, 2009, pp. 171–184.

  155. On the range of the iterated Euler function, F. Luca and C. Pomerance, Combinatorial Number Theory, Proceedings of Integers Conference 2007, de Gruyter, Berlin, 2009, pp. 101–116.

  156. On Giuga numbers, F. Luca, C. Pomerance, and I. E. Shparlinski, Int. J. Mod. Math., 4 (2009), 13–28.

  157. On the distribution of sociable numbers, M. Kobayashi, P. Pollack, and C. Pomerance, J. Number Theory 129 (2009), 1990–2009.

  158. On the Artin–Carmichael primitive root problem on average, S. Li and C. Pomerance, Mathematika 55 (2009), 167–176.

  159. On the smallest pseudopower, J. Bourgain, S. V. Konyagin, C. Pomerance, and I. E. Shparlinski, Acta Arith. 140 (2009), 43–55.

  160. A remark on Giuga's conjecture and Lehmer's totient problem, W. D. Banks, C. W. Nevans, and C. Pomerance, Albanian J. Math. 3 (2009), 81–85.

  161. On the distribution of pseudopowers, S. V. Konyagin, C. Pomerance, and I. E. Shparlinski, Canad. J. Math., 62 (2010), 582–594.

  162. Rank statistics for a family of elliptic curves over a function field, C. Pomerance and I. E. Shparlinski, Pure Appl. Math. Q., 6 (2010), 21–40.

  163. Primality testing: variations on a theme of Lucas, C. Pomerance, in the Proceedings of the 13th Meeting of the Fibonacci Association, Congressus Numerantium 201 (2010), 301–312.

  164. Error estimates for the Davenport–Heilbronn theorems, K. Belabas, M. Bhargava, and C. Pomerance, Duke Math. J. 153 (2010), 173–210.

  165. Common values of the arithmetic functions φ and σ, K. Ford, F. Luca, and C. Pomerance, Bull. London Math. Soc., 42 (2010), 478–488.

  166. On Carmichael numbers in arithmetic progressions, W. D. Banks and C. Pomerance, J. Australian Math. Soc., 28 (2010), 313–321.

  167. On the radical of a perfect number, F. Luca and C. Pomerance, New York Journal of Math., 16 (2010), 23–30.

  168. On the asymptotic effectiveness of Weil descent attacks, K. Karabina, A. Menezes, C. Pomerance, and I. Shparlinski, J. Math. Crypt., 4 (2010), 175–191.

  169. Fixed points for discrete logarithms, M. Levin, C. Pomerance, and K. Soundararajan, ANTS IX Proceedings, LNCS 6197 (2010), 6–15.

  170. Remarks on the Pólya–Vinogradov inequality, C. Pomerance, Integers (Proceedings of the Integers Conference, October 2009), 11A (2011), Article 19, 11pp.

  171. Fibonacci integers, F. Luca, C. Pomerance, and S. Wagner, J. Number Theory 131 (2011), 440–457.

  172. On composite integers n for which φ(n )|n –1, F. Luca and C. Pomerance, Boletin de la Sociedad Matemática Mexicana 17 (2011), 13–21.

  173. Primitive sets with large counting functions, G. Martin and C. Pomerance, Publ. Math. Debrecen, 77 (2011), 521–530.

  174. Multiplicative properties of sets of residues, C. Pomerance and A. Schinzel, Moscow J. Combinatorics and Number Theory, 1 (2011), 52–66.

  175. On numbers n dividing the n th term of a linear recurrence, J. J. Alba González, F. Luca, C. Pomerance, and I. E. Shparlinski, Proc. Edinburgh Math. Soc., 55 (2012), 271–289.

  176. Prime-perfect numbers, P. Pollack and C. Pomerance, Integers (Selfridge memorial issue), 12A (2012), A14, 19 pp.

  177. Infinitude of elliptic Carmichael numbers, A. Ekstrom, C. Pomerance, and D. S. Thakur, J. Australian Math. Soc., 92 (2012), 45–60.

  178. Product-free sets with high density, P. Kurlberg, J. C. Lagarias, and C. Pomerance, Acta Arith., 155 (2012), 163–173.

  179. The average order of elements in the multiplicative group of a finite field, Y. Hu and C. Pomerance, Involve, 5-2 (2012), 229–236.

  180. On sets of integers which are both sum-free and product-free, P. Kurlberg, J. C. Lagarias, and C. Pomerance, Integers (Proceedings of the 2011 Integers Conference), 12B (2012), A4, 9 pp.

  181. On congruences of the form σ(n ) ≡ a (mod n ), A. Anavi, P. Pollack, and C. Pomerance, IJNT, 9 (2012), 115–124.

  182. On a problem of Arnold: the average multiplicative order of a given integer, P. Kurlberg and C. Pomerance, Algebra and Number Theory, 7 (2013), 981–999.

  183. Sets of monotonicity for Euler's totient function, P. Pollack, C. Pomerance, and E. Treviño, Ramanujan J., 30 (2013), 379–398.

  184. On the distribution of some integers related to perfect and amicable numbers, P. Pollack and C. Pomerance, Colloq. Math., 130 (2013), 169–182.

  185. The maximal density of product-free sets in Z/nZ, P. Kurlberg, J. C. Lagarias, and C. Pomerance, Int. Math. Res. Not. IMRN, 2013 (2013) #4, 827–845 (first published online February 14, 2012 doi:10.1093/imrn/rns014).

  186. On balanced subgroups of the multiplicative group, C. Pomerance and D. Ulmer, in Number theory and related fields, in memory of Alf van der Poorten, J. M. Borwein, I. Shparlinski, and W. Zudlin, eds., Springer Proceedings in Mathematics and Statistics 43 (2013), 253–270.

  187. Paul Erdős and the rise of statistical thinking in elementary number theory, P. Pollack and C. Pomerance, pp. 515–523 in Erdős Centennial, L. Lovász, I. Z. Ruzsa, and V. T. Sós, eds., János Bolyai Math. Soc. and Springer-Verlag, Hungary, 2013.

  188. On primes recognizable in deterministic polynomial time, S. Konyagin and C. Pomerance, pp. 159–186 in vol. 1 of The mathematics of Paul Erdős, second edition, R. L. Graham, J. Nesetril, and S. Butler, eds., Springer, New York, 2013. (This article is identical to #110 except for the update found here.)

  189. Variant of a theorem of Erdős on the sum-of-proper-divisors function, C. Pomerance and H.-S. Yang, Math. Comp., 83 (2014), 1903–1913.

  190. Sierpiński and Carmichael numbers, W. Banks, C. Finch, F. Luca, C. Pomerance, and P. Stănică, Trans. Amer. Math. Soc., to appear.

  191. Square values of Euler's function, P. Pollack and C. Pomerance, Bull. London Math. Soc., to appear; online as doi: 10.1112/blms/bdt097.

  192. On the local behavior of the order of appearance in the Fibonacci sequence, F. Luca and C. Pomerance, IJNT, 10 (2014), 915–933; online as DOI: 10.1142/S1793042114500079.

  193. On integers which are the sum of a power of 2 and a polynomial value, F. Luca, C. Gustavo Moreira, and C. Pomerance, Bull. Brazilian Math. Soc., to appear.

  194. On the range of Carmichael's universal exponent function, F. Luca and C. Pomerance, Acta Arith., 162 (2014), 289–308.

  195. Generating random factored Gaussian integers, easily, N. Lebowitz-Lockard and C. Pomerance, submitted for publication.

  196. Divisors of the middle binomial coefficient, C. Pomerance, Amer. Math. Monthly, to appear.

  197. On amicable numbers, C. Pomerance, to appear in a Springer volume in honor of H. Maier.

  198. The range of the sum-of-proper-divisors function, F. Luca and C. Pomerance, submitted for publication.

  199. The range of Carmichael's λ-function, K. Ford, F. Luca, and C. Pomerance, submitted for publication.

  200. On the counting function of irregular primes, F. Luca, A. Pizarro-Madariaga, and C. Pomerance, submitted for publication.

    Last modified July, 2014.