757

sweety439 · 2020-10-19, 15:45

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

Viliam Furik · 2020-10-19, 20:33

Quote:

Originally Posted by sweety439

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?

kar_bon · 2020-10-19, 20:40

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.

Stargate38 · 2020-11-01, 23:22

www.numbersaplenty.com/757

If you click on one of the categories (i.e. strong prime), it has links to OEIS and Wikipedia at the bottom of the page (under Useful Links), so the information is correct (unless the linked sequence and/or Wiki page is in error). I'm sure that's where Sweety439 is getting that info.

2020-10-19, 15:45	#1
sweety439 Nov 2016 2²×691 Posts	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

2020-10-19, 20:40	#3
kar_bon Mar 2006 Germany 2·1,433 Posts	That's the issue of his information all the time: not giving any search ranges or any sources. From the CRUS project 756757^n+1 is searched to n=100k, so not that high so far. And the n-value for 757758^n-1 can be found here as n=50563.

2020-11-01, 23:22	#4
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 631 Posts	www.numbersaplenty.com/757 If you click on one of the categories (i.e. strong prime), it has links to OEIS and Wikipedia at the bottom of the page (under Useful Links), so the information is correct (unless the linked sequence and/or Wiki page is in error). I'm sure that's where Sweety439 is getting that info.