Program for Sage [closed]

asked 2018-12-04 03:52:18 -0600

polistirolo gravatar image

The ec(k) numbers are so defined: ec(k)=(2^k-1)10^d+2^(k-1)-1, where d is the number of decimal digits of 2^(k-1)-1. Examples of these numbers are: 31, 157, 3115, 40952047,... I found that up to k=565.000 there is no prime of the form (2^k-1)10^d+2^(k-1)-1 which is congruent to 6 mod 7, so I conjectured that there is no prime of this form congruent to 6 mod 7. Has somebody a program for Sage for checking this conjecture further?

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Closed for the following reason duplicate question by kcrisman
close date 2018-12-06 10:48:00.653310

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slelievre gravatar imageslelievre ( 2018-12-06 11:20:59 -0600 )edit