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Old 2020-10-19, 15:45   #1
sweety439's Avatar
Nov 2016

234710 Posts
Default 757

757 is irregular prime
757 is de Polignac number (cannot be written as 2^n+p with prime p)
757 is the smallest prime p such that 1/p has period length 3^3 (in decimal)
The smallest n such that Phi_n(k,k-1) is prime is 414, where k is 757 (this is the largest for k<=1024) (there are only 3 n-values <=1024 such that Phi_n(k,k-1) is prime, and both of them are even, where k is 757) (if we require n is prime, then the smallest n is 96487)
There is no known prime of the form (b-1)*b^n+1 with n>=1, where b is 757
The smallest known prime of the form b*(b+1)^n-1 is very large, where b is 757
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Old 2020-10-19, 20:33   #2
Viliam Furik
Jul 2018
Martin, Slovakia

33·7 Posts

Originally Posted by sweety439 View Post
There is no known prime of the form (b-1)*b^n+1 with n>=1, where b is 757
To what n has these numbers been tested?
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Old 2020-10-19, 20:40   #3
kar_bon's Avatar
Mar 2006

1011001000102 Posts

That's the issue of his information all the time: not giving any search ranges or any sources.

From the CRUS project 756*757^n+1 is searched to n=100k, so not that high so far.

And the n-value for 757*758^n-1 can be found here as n=50563.
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