Hmmm ... yes, a bit of similarity in runs of initial decimal digits:
...
607
1279
2203
2281
3217
4253
4423
9689
...
6972593
13466917
20996011
24036583
25964951
30402457
32582657
37156667
43112609
(?)
But why should that mean anything other than a coincidence within a larger demonstration of Benford's Law (
http://mathworld.wolfram.com/BenfordsLaw.html or
http://en.wikipedia.org/wiki/Benford's_law) over a set of numbers (_all_ known Mersenne-prime exponents, not just two specially-picked subsets) whose distribution is expected to be related to logarithms?
Looking at all the known Mersenne-prime exponents with 1-7 decimal digits (we don't yet have a complete census for 8-decimal-digit exponents), the counts by initial digit are:
1: 12
2: 7
3: 4
4: 3
5: 2
6: 3
7: 2
8: 3
9: 2
Of the 38 exponents in that range,
12/38 = 32% start with "1",
7/38 = 18% start with "2",
4/38 = 11% start with "3".
Compare that to the ideal Benford distribution of
30.1% "1"s,
17.6% "2"s, and
12.5% "3"s.
Pretty close for such a small sample (N = 38), eh? And -- Benford's Law comes with a logical mathematical explanation -- no guessing needed!