Below is the current list of 304 exponents of Mersenne numbers less than the 12th Fermat number 2^4096+1 which have not yet been fully factored, according to https://www.mersenne.ca/. We stop at F12 because it is currently the first unfactored Fermat number.
Over time, the threshold of smallest unfactored number will gradually increase as the capabilities of SNFS increase, perhaps someday reaching F12. (Numbers will also randomly get picked off by ECM.) (Or the threshold might suddenly increase drastically with a tremendous breakthrough in factoring technology.) Click a number to see its latest status, assuming the site is and continues to be up to date. This is a big if because (among other reasons) Mersenne number factoring is a distributed project with people able to work independently and report results in various ad hoc ways.
Not listed below are the 63 exponents in the range 1213 .. 4096 which have already been fully factored, including Mersenne primes 1279 2203 2281 3217.
mersenne.ca has a pretty table giving known factors, but note that it omits exponents which have no known factors (1277 1619 1753 2137 2267 2273 2423 2521 2713 2719 2851 3049 3673 3691 3847 3881 3919 4007 4049). If the site stops existing or is not kept updated, useful as an alternative may be the Champions and first 5 holes at the Cunningham Project, though the first 5 holes of the 2,n- list might not be prime exponents (Mersenne numbers) (currently the smallest is 1207=17*71).
1213 1217 1229 1231 1237 1249 1259 1277 1283 1291 1297 1319 1367 1381 1399 1423 1429 1433 1439 1447 1451 1453 1481 1483 1489 1493 1499 1511 1523 1549 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1663 1667 1669 1697 1699 1709 1721 1733 1741 1747 1753 1759 1777 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1913 1931 1933 1949 1951 1973 1979 1987 1993 1999 2003 2011 2017 2027 2029 2039 2053 2063 2081 2083 2089 2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2207 2213 2221 2237 2239 2267 2269 2273 2287 2293 2297 2309 2333 2339 2341 2347 2371 2377 2389 2393 2399 2411 2417 2423 2437 2459 2467 2473 2477 2503 2521 2531 2539 2543 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 2671 2683 2687 2689 2693 2707 2711 2713 2719 2729 2731 2741 2753 2767 2777 2791 2797 2801 2803 2819 2833 2843 2851 2857 2861 2879 2897 2903 2917 2939 2953 2957 2963 2969 2971 2999 3001 3011 3019 3023 3049 3061 3067 3083 3109 3119 3121 3137 3163 3167 3169 3181 3187 3191 3209 3221 3229 3251 3253 3257 3271 3299 3301 3313 3319 3323 3329 3331 3343 3347 3361 3371 3373 3389 3391 3407 3433 3449 3457 3461 3463 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3557 3559 3571 3581 3583 3593 3607 3613 3617 3623 3631 3643 3659 3671 3673 3677 3691 3697 3701 3709 3719 3727 3739 3761 3767 3769 3779 3793 3797 3803 3821 3823 3847 3851 3853 3863 3877 3881 3889 3907 3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 4003 4007 4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093
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