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• W2962806999 abstract "A Wilson prime is a prime <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=application/x-tex>p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis p minus 1 right-parenthesis factorial equals minus 1 left-parenthesis mod p squared right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> <mml:mo>!</mml:mo> <mml:mo>=</mml:mo> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> <mml:mspace width=0.667em /> <mml:mo stretchy=false>(</mml:mo> <mml:mi>mod</mml:mi> <mml:mspace width=0.333em /> <mml:msup> <mml:mi>p</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(p-1)! = -1 pmod {p^2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We report on a search for Wilson primes up to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=2 times 10 Superscript 13> <mml:semantics> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>×<!-- × --></mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>13</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>2 times 10^{13}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and describe several new algorithms that were used in the search. In particular, we give the first known algorithm that computes <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis p minus 1 right-parenthesis factorial left-parenthesis mod p squared right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> <mml:mo>!</mml:mo> <mml:mspace width=0.667em /> <mml:mo stretchy=false>(</mml:mo> <mml:mi>mod</mml:mi> <mml:mspace width=0.333em /> <mml:msup> <mml:mi>p</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(p-1)! pmod {p^2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in average polynomial time per prime." @default.
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• W2962806999 date "2014-01-27" @default.
• W2962806999 modified "2023-09-27" @default.
• W2962806999 title "A search for Wilson primes" @default.
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• W2962806999 doi "https://doi.org/10.1090/s0025-5718-2014-02800-7" @default.
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