- **enzocreti**
(*https://www.mersenneforum.org/forumdisplay.php?f=156*)

- - **for which values of p this expression has the form s*2^k?**
(*https://www.mersenneforum.org/showthread.php?t=24279*)

for which values of p this expression has the form s*2^k?let be p an arbitrary prime...
can you find values of p such that (10^p-1)/9+1 has the form s*2^k? where s is a prime and k an integer >0 example p=3 does the job infact (10^3-1)/9+1 has the form 7*2^4 p=5 does not the job because (10^5-1)/9+1 has the form 2^3*3*463... |

Primes that do the job up to 103I found that the primes that do the job up to p=103 are: 3, 7, 43.
Is there some relation with the fact that 10^r+333667 is prime for r=3,7 and 43 and no other prime r up to r=26.000? |

[QUOTE=enzocreti;513344]let be p an arbitrary prime...
can you find values of p such that (10^p-1)/9+1 has the form s*2^k?[/QUOTE] 2, 3, 7, 229, 1579 |

I note that
if n > 3 then N = ((10^n - 1)/9 + 1)/8 is an odd integer. Also, n need not be prime for N to be prime. [code]? for(i=4,1000,n=1+(10^i-1)/9;n=n/8;if(ispseudoprime(n),print(i))) 4 7 16 43 58 106 160 229 628[/code] |

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