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New Mersenne Prime discovered (probably)

(www.mersenne.org)
359 points sdsykes | 5 comments | 16 Oct 24 11:51 UTC | HN request time: 0.622s | source
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stevefan1999 ◴[19 Oct 24 06:39 UTC] No.41886077[source]▶
But why do we have to "discover" it when we know the formula would be 2^N - 1...? Are we trying to prove a corollary or what?
replies(2): >>41886104 #>>41886109 #
1. aaronmdjones ◴[19 Oct 24 06:45 UTC] No.41886104[source]▶
Not all 2^N - 1 are prime. For example, N=18 makes 2^N - 1 = 262143, which can also be written as 3^3 * 7 * 19 * 73 (not prime).
replies(2): >>41886111 #>>41887510 #
2. stevefan1999 ◴[19 Oct 24 06:46 UTC] No.41886111[source]▶
Oh, right, all Mersenne number is in the form of 2^N -1, but Mersenne prime is Mersenne number plus being prime
replies(1): >>41887050 #
3. mort96 ◴[19 Oct 24 10:46 UTC] No.41887050[source]▶
And we look for Mersenne primes, AFAIU, mainly because Mersenne numbers are more likely to be prime than other numbers, so it's easier to find big primes that way.
4. umanwizard ◴[19 Oct 24 12:56 UTC] No.41887510[source]▶
A lot simpler example is 2^4-1=5*3
replies(1): >>41890565 #
5. lupire ◴[19 Oct 24 20:32 UTC] No.41890565[source]▶
2^11-1 (prime power) for a less trivial example