WebMar 29, 2016 · In special cases, the number of bases can easily be calculated, for example the case n = ( 4 k + 3) ( 8 k + 5) , where 4 k + 3 and 8 k + 5 are primes, we have ϕ ( n) 4 … WebIf n and 2 n − 1 are primes , where n > 3 , then p = n ⋅ ( 2 n − 1) is a pseudoprime to base 3 . Claim: If p is an odd prime not dividing a 2 − 1, then m := a 2 p − 1 a 2 − 1 is a pseudoprime base a. Proof: We know a p ≡ a mod p, so we also know a 2 p ≡ a 2 mod p. So we know that p ∣ ( a 2 p − a 2).

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WebThe Baillie–PSW test is a combination of a strong Fermat probable prime test (that means Miller-Rabin) to base 2 and a strong Lucas probable prime test. The Fermat and Lucas test each have their own list of pseudoprimes, that is, composite numbers that pass the test. For example, the first ten strong pseudoprimes to base 2 are WebApr 1, 2005 · We conjecture that there exist no C3-spsp's < 1024 to the first 12 prime bases with heights ≥ 10 9 and so that ψ12 = 3186 65857 83403 11511 67461 (24 digits) = 399165290221 ·798330580441, which... hosting stockbox photo down

number theory - Constructing pseudoprimes to the base 3.

WebA strong pseudoprime to base a is always an Euler–Jacobi pseudoprime, an Euler pseudoprime and a Fermat pseudoprime to that base, but not all Euler and Fermat … WebMar 24, 2024 · A strong pseudoprime to the base is also an Euler pseudoprime to the base (Pomerance et al. 1980). The strong pseudoprimes include some Euler … WebOct 1, 2003 · The main idea for finding these Carmichael numbers is that we loop on the largest prime factor q 3 and propose necessary conditions on n to be a strong … psychomotor agitation mse