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Old 2021-01-20, 09:43   #1
bur
 
Aug 2020

53 Posts
Default 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.
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Old 2021-01-20, 12:51   #2
bur
 
Aug 2020

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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
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Old 2021-01-20, 21:52   #3
Batalov
 
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Mar 2008
Phi(4,2^7658614+1)/2

100100011011112 Posts
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Quote:
Originally Posted by bur View Post
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)
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Old 2021-01-21, 07:36   #4
bur
 
Aug 2020

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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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