Do 2^p-1 numbers ever have the same first prime factor?
 

Looking at the small sample from [url]http://oeis.org/A136030[/url] - 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 [url]http://factordb.com/[/url] 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?

[QUOTE=a nicol;463973]Looking at the small sample from [url]http://oeis.org/A136030[/url] - 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 [url]http://factordb.com/[/url] 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?[/QUOTE]

any coprime exponents can't share any factor.

[QUOTE=science_man_88;463978]any coprime exponents can't share any factor.[/QUOTE]

Thank you!