2^1571237 · (1153# - 1) + 1 - why was it constructed like that?

bur · 2021-01-20, 09:43

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.

bur · 2021-01-20, 12:51

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.

Batalov · 2021-01-20, 21:52

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)

bur · 2021-01-21, 07:36

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.

2021-01-20, 09:43	#1
bur Aug 2020 53 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 53 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

2021-01-21, 07:36	#4
bur Aug 2020 53 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.