ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 06 Dec 2018 11:20:59 -0600Program for Sagehttp://ask.sagemath.org/question/44576/program-for-sage/ 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?Tue, 04 Dec 2018 03:52:18 -0600http://ask.sagemath.org/question/44576/program-for-sage/Comment by slelievre for <p>The ec(k) numbers are so defined:
ec(k)=(2^k-1)<em>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)</em>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?</p>
http://ask.sagemath.org/question/44576/program-for-sage/?comment=44604#post-id-44604Duplicate of [Ask Sage question 44575](https://ask.sagemath.org/question/44575).Thu, 06 Dec 2018 11:20:59 -0600http://ask.sagemath.org/question/44576/program-for-sage/?comment=44604#post-id-44604