I have read in this link if it is true that $2^{282589933}-1$ is a new Mersenne prime which was discovered in 07 december 2018 , Really I want to know how this was tested to be a prime number ?
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3Lucas Lehmer Test – Dubs Dec 21 '18 at 20:27
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Pretty much every new very large prime we discover is a Mersenne prime, verified the way Dubs mentioned. Of course, RSA encryption needs to make use of less obvious very large primes, not obtainable using any standard method. – J.G. Dec 21 '18 at 20:51
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There is a typo in the exponent – Peter Dec 23 '18 at 12:31
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I can't post this as a comment due to reputation, but this question is a duplicate of How to verify large Mersenne Primes
As mentioned by Dubs, the process used is called the Lucas-Lehmer Primality Test
Theorem (Lucas-Lehmer Primality). Let p be an odd prime and define the sequence S = {s$_i$ | $\forall$i $\in$ I$_n$} such that s$_1$ = 4 and s$_n$ = s$_n$$_-$$_1$$^2$ - 1, where I$_n$ denotes the index set. The p-th Mersenne number, denoted M$_p$ = 2$^p$-1 , is said to be a prime if and only if S(p-1) = 0 mod M$_p$ .
A proof of the theorem is explained in the link above.
Victoria M
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