For what composite numbers x will a x &#x2212;<!-- − -->

Davon Irwin

Davon Irwin

Answered question

2022-06-06

For what composite numbers x will a x 1 1 ( mod x ) for a [ 2 , n ]?
Can we generate xs that give false positives to the Rabin-Miller test for the first, say 10, consecutive integers a > 1?

Answer & Explanation

Braedon Rivas

Braedon Rivas

Beginner2022-06-07Added 24 answers

This is actually two different questions. The Rabin-Miller test is more stringent than simply requiring that a x 1 1 (mod x).
For instance, 294409 = 37 × 73 × 109, which gives false positives for all a < 37. I think the smallest such Carmichael number is 29341 = 13 × 37 × 61,

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