20230515, 08:35  #1 
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May 2018
1022_{8} Posts 
Find factors with k = 2^n  1 = Mersenne prime
Examples:
n = 2, p = 5, k = 2^{n}  1 = M2, 2kp + 1 = 31 = M5; n = 3, p = 929, k = 2^{n}  1 = M3, 2kp + 1 = 13007 is a factor of M929; n = 5, p = 1973, k = 2^{n}  1 = M5, 2kp + 1 = 122327 is a factor of M1973; n = 7, p = 37097, k = 2^{n}  1 = M7, 2kp + 1 = 9422639 is a factor of M37097; n = 13, p = 1946669, k = 2^{n}  1 = M13, 2kp + 1 = 31890331559 is a factor of M1946669; etc. 
20230515, 09:58  #3 
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May 2018
2×5×53 Posts 
Find also factors with k given as a product of Mersenne primes (not necessarily distinct ones) k = 2^{m}(2^{n}^{1}  1)(2^{n}^{2}  1)...
The challenge is to find a NEW factor. 
20230517, 08:59  #5 
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May 2018
2·5·53 Posts 
Note that if there are several entries for a given n value, the corresponding leading entry for said n is the one with the smallest p value.

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