Is every ec prime with k congruent to 7 mod 10 of the form 900s+163?











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A conjecture about numbers of the form $10^{m}(2^{k}−1)+2^{k-1}−1$, where $m$ is the number of decimal digits of $ 2^{k-1}$.
In this question ec numbers are introduced. Ec(7) for example is $12763$ obtained by the concatenation of two consecutive Mersenne numbers. My question is:
is every ec prime with k congruent to 7 mod 10 of the form $900s+163$?



The examples known are for $k=7,67,360787$.






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    A conjecture about numbers of the form $10^{m}(2^{k}−1)+2^{k-1}−1$, where $m$ is the number of decimal digits of $ 2^{k-1}$.
    In this question ec numbers are introduced. Ec(7) for example is $12763$ obtained by the concatenation of two consecutive Mersenne numbers. My question is:
    is every ec prime with k congruent to 7 mod 10 of the form $900s+163$?



    The examples known are for $k=7,67,360787$.






    number-theory







    share|cite|improve this question







    New contributor




    paolo galli is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.






















      up vote
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      down vote

      favorite









      up vote
      0
      down vote

      favorite











      A conjecture about numbers of the form $10^{m}(2^{k}−1)+2^{k-1}−1$, where $m$ is the number of decimal digits of $ 2^{k-1}$.
      In this question ec numbers are introduced. Ec(7) for example is $12763$ obtained by the concatenation of two consecutive Mersenne numbers. My question is:
      is every ec prime with k congruent to 7 mod 10 of the form $900s+163$?



      The examples known are for $k=7,67,360787$.






      number-theory







      share|cite|improve this question







      New contributor




      paolo galli is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      A conjecture about numbers of the form $10^{m}(2^{k}−1)+2^{k-1}−1$, where $m$ is the number of decimal digits of $ 2^{k-1}$.
      In this question ec numbers are introduced. Ec(7) for example is $12763$ obtained by the concatenation of two consecutive Mersenne numbers. My question is:
      is every ec prime with k congruent to 7 mod 10 of the form $900s+163$?



      The examples known are for $k=7,67,360787$.






      number-theory




      number-theory






      share|cite|improve this question







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      paolo galli is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      share|cite|improve this question







      New contributor




      paolo galli is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      share|cite|improve this question






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