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

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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
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Quote:
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
 
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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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Old 2020-11-01, 23:22   #4
Stargate38
 
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"Daniel Jackson"
May 2011
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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.
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