Some special factorization status of generalized repunits

[sweety439]

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)

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)
-2      29, 41, 53, 3329          619                                                               499
3       11, 23, 131               349, 661 (a little > 1.3)                                         569
-3      (not exist since no 2*p+1 divides (3^p+1)/4)
6       11                        67, 353                                                           347
-6      89, 173                   23                                                                (none known)
10      (none known)              17 (a little > 1.3), 71, 211                                      193, 223
-10     29                        (none known)                                                      (none known)
12      131                       311?                                                              23, 193, 239
-12     (not exist since no 2*p+1 divides (12^p+1)/13)

[sweety439]

2,727- 122/98 = 1.244897959183...
2,1061- 177/143 = 1.237762237762...
6,353- 155/120 = 1.291666666666...
10,211- 118/93 = 1.268817204301...

All them are in the range (1.2,1.3), the "most beautiful" range

and

2,523- 90/69 = 1.304347826086... ("a little" larger than 1.3)

However, base 3 and 12 have no known prime in this range:

3,349- 87/80 = 1.0875 (too small)
3,373- 106/73 = 1.452054794520... (too large)
3,661- 182/134 = 1.358208955223... (too large)

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3,569- P115*P116
6,347- P96*P96
10,193- P54*P55
10,223- P105*P107
10,337- P101*P102 (recently found!!!)
12,193- P77*P77
12,239- P101*P102

However, base 2 has no known example with large two prime factors are P(n)*P(n) or P(n)*P(n+1) or P(n)*P(n+2)

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(2^p-1)/(2*p+1) is prime for p = 11, 23, 83, 131, 3359
(3^p-1)/2/(2*p+1) is prime for p = 11, 23, 131
(6^p-1)/5/(2*p+1) is prime for p = 11
(12^p-1)/11/(2*p+1) is prime for p = 131

However, base 10 has no known such example, i.e. there is no known prime p such that (10^p-1)/9/(2*p+1) is prime