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Old 2020-10-15, 22:11   #1
sweety439
 
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Default Some special factorization status of generalized repunits

The generalized repunits (b^p-1)/(b-1) with a given factorization status

A = Semiprime and divisible by 2*p+1
B = Semiprime and the two prime factors are both large ((number of digits of the larger prime) / (number of digits of the smaller prime) < 1.3)
C = The largest two prime factors are very close ((the larger prime) / (the smaller prime) < 100)

Code:
Base    A                         B                                                                 C
2       11, 23, 83, 131, 3359     67 (a little > 1.3), 101, 137, 149, 523, 727, 1061, 1277?         277 (a little > 100), 397 (all of the largest three prime factors)
3       11, 23, 131               349, 661 (a little > 1.3)                                         569
6       11                        67, 353                                                           347
10      (none known)              17 (a little > 1.3), 71, 211                                      193, 223
12      131                       311?                                                              23, 193, 239
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