Carl Pomerance

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Carl Pomerance is affiliated with the following schools: Harvard University, Brown University, Dartmouth College, University of Georgia

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Carl Pomerance

Mathematics

#490

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#961

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#220

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Number Theory

#32

World Rank

#51

Historical Rank

#11

USA Rank

Measure Theory

#1410

World Rank

#1769

Historical Rank

#488

USA Rank

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Mathematics

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Bachelors Mathematics Brown University

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According to Wikipedia, Carl Bernard Pomerance is an American number theorist. He attended college at Brown University and later received his Ph.D. from Harvard University in 1972 with a dissertation proving that any odd perfect number has at least seven distinct prime factors. He joined the faculty at the University of Georgia, becoming full professor in 1982. He subsequently worked at Lucent Technologies for a number of years, and then became a distinguished Professor at Dartmouth College.

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Carl Pomerance's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Prime Numbers: A Computational Perspective (2002) (857)
The Development of the Number Field Sieve (1994) (575)
There are infinitely many Carmichael numbers (1994) (381)
On a problem of Oppenheim concerning “factorisatio numerorum” (1983) (345)
Advances in Cryptology — CRYPTO ’87 (2000) (290)
The Quadratic Sieve Factoring Algorithm (1985) (244)
Factoring integers with the number field sieve (1993) (234)
A Tale of Two Sieves (1998) (233)
The Riemann Zeta-Function and the One-Dimensional Weyl-Berry Conjecture for Fractal Drums (1993) (195)
A rigorous time bound for factoring integers (1992) (135)
A search for Wieferich and Wilson primes (1997) (126)
The pseudoprimes to 25⋅10⁹ (1980) (121)
Carmichael's lambda function (1991) (120)
Fast, Rigorous Factorization and Discrete Logarithm Algorithms (1987) (114)
Average case error estimates for the strong probable prime test (1993) (99)
Counterexamples to the modified Weyl–Berry conjecture on fractal drums (1996) (84)
On the Normal Behavior of the Iterates Of some Arithmetic Functions (1990) (81)
Reduction of Huge, Sparse Matrices over Finite Fields Via Created Catastrophes (1992) (79)
On the distribution of amicable numbers. (1977) (74)
POPULAR VALUES OF EULER'S FUNCTION (1980) (74)
A Pipeline Architecture for Factoring Large Integers with the Quadratic Sieve Algorithm (1988) (74)
The Search for Prime Numbers. (1982) (70)
Period of the power generator and small values of Carmichael's function (2001) (67)
On the distribution of amicable numbers. II. (1977) (66)
A hyperelliptic smoothness test. I (1993) (66)
On the binary expansions of algebraic numbers (2003) (66)
Recent developments in primality testing (1981) (65)
Unusually large gaps between consecutive primes (1990) (63)
Timed Fair Exchange of Standard Signatures (2003) (48)
On the normal number of prime factors of $\phi(n)$ (1985) (48)
On the periods of the linear congruential and power generators (2004) (47)
A note on the least prime in an arithmetic progression (1980) (46)
The Role of Smooth Numbers in Number Theoretic Algorithms (1995) (46)
View-Obstruction Problems, III (1984) (45)
Two contradictory conjectures concerning Carmichael numbers (2002) (44)
On composite n for which φ(n) n -1 (1977) (42)
On the distribution of pseudoprimes (1981) (42)
Timed Fair Exchange of Standard Signatures: [Extended Abstract] (2003) (42)
Combinatorial number theory (1996) (40)
Cryptology and Computational Number Theory (1997) (40)
Sieving by large integers and covering systems of congruences (2005) (39)
On generalizing Artins conjecture on primitive roots to composite moduli (2003) (38)
On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions ϕ and σ (2002) (37)
Error estimates for the Davenport-Heilbronn theorems (2010) (37)
Multiplicative Structure of Values of the Euler Function (2004) (36)
Rigorous discrete logarithm computations in finite fields via smooth polynomials (1997) (36)
On locally repeated values of certain arithmetic functions. II (1987) (35)
Odd perfect numbers are divisible by at least seven distinct primes (1974) (35)
Advances in cryptology -- CRYPTO '87 : proceedings (1988) (35)
Irreducible radical extensions and Euler-function chains (2007) (35)
On the number of distinct values of Euler's φ-function (1988) (34)
The distribution of Lucas and elliptic pseudoprimes (1991) (33)
On the difficulty of finding reliable witnesses (1994) (33)
The Mathematics of Paul Erdős I (2013) (32)
Very short primality proofs (1987) (32)
Smooth Orders and Cryptographic Applications (2002) (31)
Multiply perfect numbers, mersenne primes, and effective computability (1977) (31)
Remarks on the Pólya–Vinogradov Inequality (2011) (30)
On the number of false witnesses for a composite number (1986) (30)
On Primes Recognizable in Deterministic Polynomial Time (2013) (29)
Automaticity II: Descriptional Complexity in the Unary Case (1997) (28)
On the largest prime factor of a Mersenne number (2004) (28)
On a problem of Arnold: The average multiplicative order of a given integer (2011) (28)
The expected number of random elements to generate a finite abelian group (2002) (27)
Smooth numbers and the quadratic sieve (2008) (26)
The probability that a random probable prime is composite (1989) (26)
A Hyperelliptic Smoothness Test, II (2002) (25)
On locally repeated values of certain arithmetic functions, I (1985) (25)
ON THE PROBLEM OF UNIQUENESS FOR THE MAXIMUM STIRLING NUMBER(S) OF THE SECOND KIND (2001) (25)
On numbers n dividing the nth term of a linear recurrence (2010) (25)
SOME NEW RESULTS ON ODD PERFECT NUMBERS (1975) (25)
Rigorous, subexponential algorithms for discrete logarithms over finite fields (1992) (24)
A new lower bound for the pseudoprime counting function (1982) (24)
On the Distribution in Residue Classes of Integers with a Fixed Sum of Digits (2005) (23)
The distribution of smooth numbers in arithmetic progressions (1992) (23)
On a conjecture of Crandall concerning the qx + 1 problem (1995) (23)
Common values of the arithmetic functions ϕ and σ (2009) (22)
The arithmetic mean of the divisors of an integer (1981) (22)
On the largest prime factors ofn andn + 1 (1978) (21)
Euler's Function in Residue Classes (1998) (19)
The prime number graph (1979) (19)
Proof of D. J. Newman's coprime mapping conjecture (1980) (19)
Divisors of the Middle Binomial Coefficient (2015) (19)
On the average number of divisors of the Euler function (2007) (18)
ON SUMS INVOLVING RECIPROCALS OF THE LARGEST PRIME FACTOR OF AN INTEGER (2004) (18)
PRIMALITY TESTING: VARIATIONS ON A THEME OF LUCAS (18)
On the proportion of numbers coprime to a given integer (2008) (18)
Some problems of Erdős on the sum-of-divisors function (2016) (18)
A Mock Theta Function for the Delta-function (2009) (17)
On the largest prime factors ofn andn + 1 (1978) (17)
Fixed Points for Discrete Logarithms (2010) (17)
On the Least Prime in Certain Arithmetic Progressions (1990) (16)
On primitive divisors of Mersenne numbers (1986) (16)
The generation of random numbers that are probably prime (1988) (16)
Products of Ratios of Consecutive Integers (2005) (16)
On Giuga numbers (2009) (16)
On the radical of a perfect number (2010) (16)
Sets on which an entire function is determined by its range (1981) (16)
Counting the Integers Factorable via Cyclotomic Methods (1995) (16)
The second largest prime factor of an odd perfect number (1975) (16)
On the distribution of sociable numbers (2009) (15)
On Amicable Numbers (2015) (15)
On locally repeated values of certain arithmetic functions. III (1987) (15)
On integers $n$ for which $X^n-1$ has a divisor of every degree (2015) (14)
On the smallest pseudopower (2009) (14)
ON CARMICHAEL NUMBERS IN ARITHMETIC PROGRESSIONS (2010) (14)
On Elements of Sumsets with Many Prime Factors (1993) (14)
On the congruences $σ(n) ≡ a (mod n)$ and $n ≡ a (mod φ(n))$ (1975) (14)
The Erdős conjecture for primitive sets (2018) (13)
Computational Number Theory (2006) (13)
Elliptic Curve Arithmetic (2001) (13)
On homogeneous multiplicative hybrid problems in number theory (1988) (13)
Collinear Subsets of Lattice Point Sequences - An Analog of Szemerédi's Theorem (1980) (13)
ON CONGRUENCES OF THE FORM σ(n) ≡ a (mod n) (2013) (12)
Explicit estimates for the distribution of numbers free of large prime factors (2017) (12)
Residue classes free of values of Euler's function (2020) (12)
On compositenfor whichφ(n)∣n− 1. II (1977) (12)
Elementary thoughts on discrete logarithms (2008) (12)
An upper bound in Goldbach’s problem (1993) (12)
On the distribution of the values of Euler's function (1986) (12)
Rank statistics for a family of elliptic curves over a function field (2009) (12)
On the counting function of irregular primes (2015) (12)
The range of the sum-of-proper-divisors function (2015) (12)
SETS WITH PRESCRIBED ARITHMETIC DENSITIES (2008) (11)
Maximal height of divisors of $x\sp n-1$ (2007) (11)
The smallestn-uniform hypergraph with positive discrepancy (1987) (10)
On the composition of the arithmetic functions σ and φ (1989) (10)
Three elliptic curves with rank at least seven (1975) (10)
A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology (1987) (10)
The iterated Carmichael \lambda-function and the number of cycles of the power generator (2004) (10)
Analytic Number Theory: In Honor of Helmut Maier's 60th Birthday (2015) (9)
Small Sets Satisfying the Central Sets Theorem (2009) (9)
On the number of divisors of n (1996) (9)
Counting elliptic curves with an isogeny of degree three (2019) (9)
Variant of a theorem of Erdős on the sum-of-proper-divisors function (2013) (8)
On Balanced Subgroups of the Multiplicative Group (2012) (8)
The Finite Heine Transformation (2009) (8)
The image of Carmichael’s λ-function (2014) (8)
Review: Hans Riesel, Prime numbers and computer methods for factorization (1988) (8)
The reciprocal sum of the amicable numbers (2018) (8)
Symmetric and Asymmetric Primes (1996) (8)
A Search for Elliptic Curves With Large Rank (1974) (8)
On Pseudosquares and Pseudopowers (2007) (8)
On the Distribution of Pseudopowers (2007) (7)
Multiplicative Relations for Sums of Initial kth Powers (1985) (7)
Connected Components of the Graph Generated by Power Maps in Prime Finite Fields (2017) (7)
Numbers Divisible by a Large Shifted Prime and Large Torsion Subgroups of CM Elliptic Curves (2016) (7)
Elliptic curves with Galois-stable cyclic subgroups of order 4 (2020) (7)
Matching the natural numbers up to n with distinct multiples in another interval (1980) (7)
The Artin-Carmichael primitive root problem on average (2009) (7)
On Carmichael’s conjecture (1974) (7)
Multiplicative properties of sets of residues (2010) (7)
Sierpinski and Carmichael numbers (2014) (7)
Acknowledgment of priority: “On some problems of Mąkowski–Schinzel and Erdős concerning the arithmetical functions $\phi$ and $\sigma$” (Colloq. Math. 92 (2002), 111–130) (2012) (7)
New Ideas for Factoring Large Integers (1983) (7)
On the range of Carmichael's universal-exponent function (2014) (6)
On the solutions to φ(n) = φ(n + k) (1999) (6)
On the asymptotic effectiveness of Weil descent attacks (2010) (6)
Squarefree smooth numbers and Euclidean prime generators (2016) (6)
On the local behavior of the order of appearance in the Fibonacci sequence (2014) (6)
Square values of Euler's function (2014) (6)
Divisor-sum fibers (2017) (6)
Finding the group structure of elliptic curves over finite fields (2005) (6)
On the distribution of some integers related to perfect and amicable numbers (2013) (6)
Lecture Notes on Primality Testing and Factoring: A Short Course at Kent State University (1984) (6)
AN ANALOGUE OF GRLMM ' S PROBLEM OF FINDING DISTINCT PRIME FACTORS OF CONSECUTIVE INTEGERS (1983) (6)
Combinatorial number theory : proceedings of the 'Integers Conference 2005' in celebration of the 70th birthday of Ronald Graham, Carrollton, Georgia, October 27-30, 2005 (2007) (5)
Small Values of the Carmichael Function and Cryptographic Applications (2001) (5)
The Quadratic Sieve Algorithm (1985) (5)
Prime-Perfect Numbers (2012) (5)
Corrigendum to: ``Period of the power generator and small values of Carmichael's function'' [Math. Comp. 70 (2001), no. 236, 1591--1605; MR1836921 (2002g:11112)] (2002) (4)
Coprime matchings (2021) (4)
Product-free sets with high density (2011) (4)
ON THE COMPOSITION OF SOME ARITHMETIC FUNCTIONS , II (2005) (4)
On a tiling problem of R.B. Eggleton (1977) (4)
Proof of the Sheldon Conjecture (2019) (4)
On multiply perfect numbers with a special property. (1975) (4)
On the Density of Integral Sets with Missing Differences (2009) (4)
On primes and practical numbers (2020) (4)
Sums and Differences of the Coordinates of Points on Modular Hyperbolas (2009) (4)
Primitive sets with large counting functions (2010) (4)
On Locally Repeated Values of Certain Arithmetic Functions, IV (1997) (4)
Primes in prime number races (2018) (3)
Corrigendum: “The distribution of Lucas and elliptic pseudoprimes” [Math. Comp. 57 (1991), no. 196, 825–838; MR1094951 (92h:11081)] (1993) (3)
ON THE RANGE OF THE ITERATED EULER FUNCTION (2008) (3)
The aliquot constant, after Bosma and Kane (2018) (3)
Long gaps in sieved sets (2018) (3)
Density of Singular Pairs of Integers (2018) (3)
COUNTING INTEGERS WITH A SMOOTH TOTIENT (2018) (3)
On composite integers n for which '(n) j n 1 (2009) (3)
Triangles with prime hypotenuse (2017) (3)
A note on square totients (2014) (3)
Sets of monotonicity for Euler’s totient function (2013) (3)
Subexponential Factoring Algorithms (2001) (3)
Frobenius Numbers of Generalized Fibonacci Semigroups (2009) (3)
A generalization of primitive sets and a conjecture of Erd\H{o}s (2020) (2)
The Maximal Density of Product-Free Sets in ℤ/nℤ (2011) (2)
The Briscoe Center for American History (1975) (2)
On the average number of groups of square-free order (1987) (2)
Corrigendum: The Distribution of Lucas and Elliptic Pseudoprimes (1993) (2)
Nearly parallel vectors (1979) (2)
Column-to-Row Operations on Partitions: The Envelopes (2009) (2)
Progress towards a nonintegrality conjecture (2019) (2)
Problems: 10330-10337 (1993) (2)
On a Conjecture of R.L. Graham (1994) (2)
The average order of elements in the multiplicative group of a finite field (2012) (2)
Fibonacci Integers (2010) (2)
A note on Carmichael numbers in residue classes (2021) (2)
Advanced Problems: 6144-6149 (1977) (2)
Generating random factored Gaussian integers, easily (2015) (1)
Coprime permutations (2022) (1)
THE FIRST FUNCTION AND ITS ITERATES (2016) (1)
Advanced Problems: 6670-6672 (1991) (1)
Fast Algorithms for Large-Integer Arithmetic (2001) (1)
Improved error bounds for the Fermat primality test on random inputs (2016) (1)
Symmetric Primes Revisited (2019) (1)
ON THE EQUATION φ(n) = φ(n+ 1) (2019) (1)
On the Euler Product of Some Zeta Functions (2009) (1)
IV.3 Computational Number Theory (2010) (1)
The Ubiquity of Prime Numbers (2001) (1)
On the Parity of the Number of Small Divisors of n (2015) (1)
The Book of Prime Number Records. By Paulo Ribenboim (1989) (1)
Cyclotomic Coincidences (2019) (1)
Local Behavior of the Composition of the Aliquot and Co-Totient Functions (2016) (1)
On integers which are the sum of a power of 2 and a polynomial value (2014) (1)
On the Critical Exponent for k-Primitive Sets (2020) (1)
Paul Erdős and the Rise of Statistical Thinking in Elementary Number Theory (2013) (1)
Avoiding Geometric Progressions in the Integers (2014) (1)
On a class of relatively prime sequences (1978) (1)
On a nonintegrality conjecture (2021) (1)
Some thoughts on pseudoprimes (2021) (0)
Combinatorial number theory : proceedings of the "Integers Conference 2011", Carrollton, Georgia, USA, October 26-29, 2011 (2009) (0)
The Man Who Loved Problems: Richard K. Guy (2022) (0)
Advanced Problems: 6601-6603 (1989) (0)
Multiplicative properties of sets of residues C . (2011) (0)
Heron Sequences and Their Modifications (2009) (0)
Finding Almost Squares III (2009) (0)
A Baseball Giant, A Math Giant, and the Epsilon in the Middle (2002) (0)
Advanced Problems: 6036-6041 (1975) (0)
Permutations with arithmetic constraints (2022) (0)
On the least prime incertain arithmetic (2008) (0)
On integers which are the sum of a power of 2 and a polynomial value (2014) (0)
Phi, primorials, and Poisson (2020) (0)
Unitary untouchable numbers (2012) (0)
#A82 INTEGERS 18 (2018) DENSITY OF SINGULAR PAIRS OF INTEGERS (2018) (0)
Number-Theoretical Tools (2001) (0)
Publications of Ron L. Graham (2007) (0)
Ronald Lewis Graham (1935–2020) (2021) (0)
ACKNOWLEDGMENT OF PRIORITY: "ON SOME PROBLEMS OF MÅKOWSKI-SCHINZEL AND ERDéS CONCERNING THE ARITHMETICAL FUNCTIONS AND " (2012) (0)
Advanced Problems: 5928-5933 (1973) (0)
THE RANGE OF CARMICHAEL’S λ-FUNCTION (2012) (0)
Corrigendum: Long gaps in sieved sets (2023) (0)
ON UNTOUCHABLE NUMBERS AND RELATED PROBLEMS (2012) (0)
Combinatorics of Ramanujan–Slater Type Identities (2009) (0)
Sets of monotonicity for Euler’s totient function (2012) (0)
Self Generating Sets and Numeration Systems (2009) (0)
Triangles with prime hypotenuse (2017) (0)
An upper bound in Goldbach ' s problembyJean (1993) (0)
On the equation $\varphi (n)=\varphi (n+1)$ (2020) (0)
On Sets of Integers Which Are Both Sum-Free and Product-Free (2012) (0)
INTEGERS 9 Supplement ( 2009 ) ON PSEUDOSQUARES AND PSEUDOPOWERS (2009) (0)
Recognizing Primes and Composites (2001) (0)
Ja n 20 20 Phi , Primorials , and Poisson (2020) (0)
Elementary Problems: E2575-E2580 (1976) (0)
1 Sieving in a more general framework (2013) (0)
Problems: 10322-10329 (1993) (0)
Sums and Products (2018) (0)
INTEGERS 22 (2022) COPRIME PERMUTATIONS (2022) (0)
The denominators of the Bernoulli numbers (2021) (0)
Primitive roots : a survey (New Aspects of Analytic Number Theory) (2002) (0)
Eigenvalues of the Laplacian on domains with fractal boundary (2019) (0)
On a problem of Evelyn--Linfoot and Page in additive number theory (2022) (0)
Number Theory (1999) (0)
Linear Equations Involving Iterates of σ (N) (2009) (0)
The William Lowell Putnam Mathematical Competition 2001–2016 (2020) (0)
Convergence Rates for Runlength Constrained Capacities (2001) (0)
INTEGERS 22 (2022) COPRIME MATCHINGS (2022) (0)
Maier Matrices Beyond Z (2009) (0)
Math 75 NOTES on finite fields (2014) (0)
LOWER BOUNDS ON THE PERIOD OF SOME PSEUDORANDOM NUMBER GENERATORS PÄR KURLBERG AND CARL POMERANCE (2007) (0)
On the distribution of champs (1999) (0)
Preface to the John Selfridge Memorial Issue (2012) (0)
Progress towards a nonintegrality conjecture (2019) (0)
1 The convolution inverse of an arithmetic function (2013) (0)
Algorithms for the Multiplication Table Problem (2019) (0)

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Published Works

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