The primality of 𝑅1031

Williams, H. C.; Dubner, Harvey

doi:10.1090/s0025-5718-1986-0856714-3

Cited by 5 publications

(4 citation statements)

References 19 publications

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“…On the other hand, testing an arbitrary number for primality depended on integer factorization. For this era, see [18,92,95]. The reader interested in large or curious primes is referred to [80] as well as [68].…”

Section: Introductionmentioning

confidence: 99%

Elliptic Curves and Primality Proving

Atkin¹,

Morain²

1993

Mathematics of Computation

123

179

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Abstract. The aim of this paper is to describe the theory and implementation of the Elliptic Curve Primality Proving algorithm.Problema, números primos a compositis dignoscendi, hosque in factores suos primos resolvendi, ad gravissima ac utilissima totius arithmeticae pertinere, et geometrarum turn veterum turn recentiorum industriam ac sagacitatem occupavisse, tarn notum est, ut de hac re copióse loqui superfluum foret.C. F. Gauss [38, Art. 329]

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Section: Introductionmentioning

confidence: 99%

Elliptic Curves and Primality Proving

Atkin¹,

Morain²

1993

Mathematics of Computation

123

179

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“…For example, R 4 = 1111. Currently, the largest known prime repunit is R 1031 which was shown to be prime by Hugh Williams and Harvey Dubner in 1986 [10]. The repunits R 49081 , R 86453 , R 109297 , and R 270343 are all probable primes, but have not been proven prime [1].…”

Section: Notation and Basic Factsmentioning

confidence: 99%

Smith Numbers From Primes with Small Digits

Costello¹

2015

Missouri J. Math. Sci.

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“…The only known prime repunits are R2, R19, R23 and, in the age of computers, R317 (discovered by and R1031 (discovered by Williams & Dubner in 1986).…”

Section: Recordmentioning

confidence: 99%

The Little Book of Bigger Primes

Ribenboim¹

2004

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The primality of 𝑅1031

Abstract: Abstract. A description is given of a technique for proving Ä1031 (= (101031 -l)/9) a prime.

Cited by 5 publications

References 19 publications

Elliptic Curves and Primality Proving

Elliptic Curves and Primality Proving

Smith Numbers From Primes with Small Digits

The Little Book of Bigger Primes

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