mersenneforum.org 2^1571237 · (1153# - 1) + 1 - why was it constructed like that?
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 2021-01-20, 09:43 #1 bur     Aug 2020 79*6581e-4;3*2539e-3 2×35 Posts 2^1571237 · (1153# - 1) + 1 - why was it constructed like that? 2^1571237 * (1153# - 1) + 1 is a new prime submitted to PrimePages. It is almost a PrimoProth, which are interesting in that they have a low weight, but why the -1? It decreases the number of small factors of N-1, but if you're after that, you might just use a prime for k.
 2021-01-20, 12:51 #2 bur     Aug 2020 79*6581e-4;3*2539e-3 2·35 Posts Correction: Should read "high weight". And now that I thought about it some more, k = 1153#-1 is a large k with few small factors but more elegant than using a 486 digit prime. Maybe that's the reason here. Last fiddled with by bur on 2021-01-20 at 12:52
2021-01-20, 21:52   #3
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

969110 Posts

Quote:
 Originally Posted by bur Maybe that's the reason here.
There doesn't appear to be any good reason for it.

Looks like a "why not" choice of a number. (if not some outright numerology)

 2021-01-21, 07:36 #4 bur     Aug 2020 79*6581e-4;3*2539e-3 2·35 Posts I checked other primes of this person and he/she often uses primes or primorials as k. So I assumed it was about having k's with many or few small factors. But you're right, maybe I'm giving it too much thought.

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