These are the largest Mersenne numbers with no factors below 2^32 In NewPGen 2.82 and GIMPS. To my understanding, GIMPS can only test up to the binary exponent of 9 digits with its current settings. There's about a 1 in a billion chance that one of them is prime: 2^(Prime Number)-1
1	2^999,999,937-1	301,029,977
2	2^999999929-1	301029975
3	2^999999893-1	301029964
4	2^999999883-1	301029961
5	2^999999797-1	301029935
6	2^999999761-1	301029924
7	2^999999757-1	301029923
8	2^999999751-1	301029921
9	2^999999739-1	301029918
10	2^999999733-1	301029916
11	2^999999677-1	301029899
12	2^999999667-1	301029896
13	2^999999613-1	301029880
14	2^999999607-1	301029878
15	2^999999599-1	301029875
16	2^999999587-1	301029872
17	2^999999541-1	301029858
18	2^999999527-1	301029854
19	2^999999503-1	301029847
20	2^999999491-1	301029843
21	2^999999487-1	301029842
22	2^999999433-1	301029825
23	2^999999391-1	301029813
24	2^999999353-1	301029801
25	2^999999337-1	301029797
26	2^999999323-1	301029792
27	2^999999229-1	301029764
28	2^999999223-1	301029762
29	2^999999197-1	301029754
30	2^999999193-1	301029753
Note: 999,999,191 is prime. 2^999,999,191-1 has a factor of 1,999,998,383 in NewPGen. It would have been 301,029,753 digits if it had no apparent factor.
31	2^999999181-1	301029750
32	2^999999163-1	301029744
33	2^999999151-1	301029741
34	2^999999137-1	301029736
35	2^999999131-1	301029735
36	2^999999113-1	301029729
37	2^999999107-1	301029727
38	2^999999103-1	301029726
39	2^999999067-1	301029715
40	2^999999059-1	301029713
41	2^999999043-1	301029708
42	2^999999029-1	301029704
43	2^999999017-1	301029700
44	2^999999001-1	301029695
45	2^999998981-1	301029689
46	2^999998971-1	301029686
47	2^999998959-1	301029683
48	2^999998957-1	301029682
49	2^999998929-1	301029674
50	2^999998921-1	301029671
These were tested by Matt Stath in March and April 2013. Thanks to Paul Jobling, who developed NewPGen 2.82. Back to Top Secret Top 50 Primes.