mersenneforum.org > Math Do 2^p-1 numbers ever have the same first prime factor?
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 2017-07-22, 09:08 #1 a nicol   Nov 2016 29 Posts Do 2^p-1 numbers ever have the same first prime factor? Looking at the small sample from http://oeis.org/A136030 - Smallest prime factor of composite Mersenne numbers: [23, 47, 233, 223, 13367, 431, 2351, 6361, 179951, 193707721, 228479, 439, 2687, 167, 11447, 7432339208719, 2550183799, 745988807, 3391, 263, 32032215596496435569, 5625767248687, 86656268566282183151, 18121, 852133201, 150287, 2349023, 730753, 359, 43441, 383] There are no duplicates here, but I have not checked further. I tried looking on http://factordb.com/ but I can't work out how to get it to only list the factors of 2^p-1 numbers - I couldn't exclude non prime odd exponents. Are there any examples of shared first prime factors?
2017-07-22, 11:20   #2
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by a nicol Looking at the small sample from http://oeis.org/A136030 - Smallest prime factor of composite Mersenne numbers: [23, 47, 233, 223, 13367, 431, 2351, 6361, 179951, 193707721, 228479, 439, 2687, 167, 11447, 7432339208719, 2550183799, 745988807, 3391, 263, 32032215596496435569, 5625767248687, 86656268566282183151, 18121, 852133201, 150287, 2349023, 730753, 359, 43441, 383] There are no duplicates here, but I have not checked further. I tried looking on http://factordb.com/ but I can't work out how to get it to only list the factors of 2^p-1 numbers - I couldn't exclude non prime odd exponents. Are there any examples of shared first prime factors?
any coprime exponents can't share any factor.

2017-07-22, 11:26   #3
a nicol

Nov 2016

2910 Posts

Quote:
 Originally Posted by science_man_88 any coprime exponents can't share any factor.
Thank you!

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