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The primality of 
Authors:
H. C. Williams and Harvey Dubner
Journal:
Math. Comp. 47 (1986), 703-711
MSC:
Primary 11Y11; Secondary 11A51
MathSciNet review:
856714
Full-text PDF Free Access
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Additional Information
Abstract: A description is given of a technique for proving a prime.
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H. Lehmer, J.
L. Selfridge, Bryant
Tuckerman, and S.
S. Wagstaff Jr., Factorizations of 𝑏ⁿ±1,
Contemporary Mathematics, vol. 22, American Mathematical Society,
Providence, R.I., 1983. 𝑏=2,3,5,6,7,10,11,12 up to high powers. MR 715603
(84k:10005)
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H.
Cohen and H.
W. Lenstra Jr., Primality testing and Jacobi
sums, Math. Comp. 42
(1984), no. 165, 297–330. MR 726006
(86g:11078), http://dx.doi.org/10.1090/S0025-5718-1984-0726006-X
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H.
Cohen and A.
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S1–S4. MR
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W. Lenstra Jr., Divisors in residue classes,
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M. Pollard, Theorems on factorization and primality testing,
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M. Pollard, A Monte Carlo method for factorization, Nordisk
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H.
C. Williams, A generalization of Lehmer’s functions,
Acta Arith. 29 (1976), no. 4, 315–341. MR 0412091
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H.
C. Williams, Factoring on a computer, Math. Intelligencer
6 (1984), no. 3, 29–36. MR 748430
(85h:11079), http://dx.doi.org/10.1007/BF03024126
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H.
C. Williams and J.
S. Judd, Determination of the primality of
𝑁 by using factors of 𝑁²±1, Math. Comp. 30 (1976), no. 133, 157–172. MR 0396390
(53 #257), http://dx.doi.org/10.1090/S0025-5718-1976-0396390-3
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H.
C. Williams and J.
S. Judd, Some algorithms for prime testing
using generalized Lehmer functions, Math.
Comp. 30 (1976), no. 136, 867–886. MR 0414473
(54 #2574), http://dx.doi.org/10.1090/S0025-5718-1976-0414473-6
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H.
C. Williams and R.
Holte, Some observations on primality
testing, Math. Comp. 32
(1978), no. 143, 905–917. MR 0476625
(57 #16184), http://dx.doi.org/10.1090/S0025-5718-1978-0476625-0
- [16]
H.
C. Williams and E.
Seah, Some primes of the form
(𝑎ⁿ-1)/(𝑎-1), Math.
Comp. 33 (1979), no. 148, 1337–1342. MR 537980
(80g:10014), http://dx.doi.org/10.1090/S0025-5718-1979-0537980-7
- [1]
- L. M. Adelman, C. Pomerance & R. S. Rumely, "On distinguishing prime numbers from composite numbers," Ann. of Math. (2), v. 117, 1983, pp. 173-206. MR 683806 (84e:10008)
- [2]
- R. P. Brent & J. H. Pollard, "Factorization of the eighth Fermat number," Math. Comp., v. 36, 1981, pp. 627-630. MR 606520 (83h:10014)
- [3]
- J. Brillhart, D. H. Lehmer & J. L. Selfridge, "New primality criteria and factorizations of
," Math. Comp., v. 29, 1975, pp. 620-647. MR 0384673 (52:5546)
- [4]
- J. Brillhart, D. H. Lehmer, John Selfridge, B. Tuckerman & S. S. Wagstaff, Jr., Factorizations of
, Up to High Powers, Contemp. Math., vol. 22, Amer. Math. Soc., Providence, R. I., 1983. MR 715603 (84k:10005)
- [5]
- H. Cohen & W. H. Lenstra, Jr., "Primality testing and Jacobi sums," Math. Comp., v. 42, 1984, pp. 297-330. MR 726006 (86g:11078)
- [6]
- H. Cohen & A. K. Lenstra, "Implementation of a new primality test," Math. Comp. (To appear.) MR 866102 (88c:11080)
- [7]
- H. Dubner & R. Dubner, "The development of a powerful, low-cost computer for number theory application," J. Recreational Math. (To appear.)
- [8]
- H. W. Lenstra, Jr., "Divisors in residue classes," Math. Comp., v. 42, 1984, pp. 331-340. MR 726007 (85b:11118)
- [9]
- J. M. Pollard, "Theorems on factorization and primality testing," Proc. Cambridge Philos. Soc., v. 76, 1974, pp. 521-528. MR 0354514 (50:6992)
- [10]
- J. M. Pollard, "A Monte Carlo method for factorization," BIT, v. 15, 1975, pp. 331-334. MR 0392798 (52:13611)
- [11]
- H. C. Williams, "A generalization of Lehmer's functions," Acta Arith., v. 29, 1976, pp. 315-341. MR 0412091 (54:220)
- [12]
- H. C. Williams, "Factoring on a computer," Math. Intelligencer, v. 6, 1984, pp. 29-36. MR 748430 (85h:11079)
- [13]
- H. C. Williams & S. Judd, "Determination of the primality of N by using factors of
," Math. Comp., v. 30, 1976, pp. 157-172. MR 0396390 (53:257)
- [14]
- H. C. Williams & S. Judd, "Some algorithms for prime testing using generalized Lehmer functions," Math. Comp., v. 30, 1976, pp. 867-886. MR 0414473 (54:2574)
- [15]
- H. C. Williams & R. Holte, "Some observations on primality testing," Math. Comp., v. 32, 1978, pp. 905-917. MR 0476625 (57:16184)
- [16]
- H. C. Williams & E. Seah, "Some primes of the form
," Math. Comp., v. 33, 1979, pp. 1337-1342. MR 537980 (80g:10014)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1986-0856714-3
PII:
S 0025-5718(1986)0856714-3
Article copyright:
© Copyright 1986 American Mathematical Society
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