Due to factordb bug I cannot upload the cert just yet, but I will this week.

The 326th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M3203[/M].

The most recent factor was found by James Hintz, and the PRP test was completed first by M91088807.

[QUOTE=GP2;506114]The 326th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M3203[/M].

The most recent factor was found by James Hintz, and the PRP test was completed first by M91088807.[/QUOTE]

It is proven in factordb

[QUOTE=axn;506133]It is proven in factordb[/QUOTE]

Okay, if I understand the drill this time, I marked that in the database as the cofactor being proven prime. It won't show up in the ECM progress report anymore as needing more curves. :smile:

[QUOTE=GP2;506114]The most recent factor was found by James Hintz, and the PRP test was completed first by M91088807.[/QUOTE]

Interesting username maybe he/she knows something about this exponent? :smile:
[url]https://mersenne.org/M91088807[/url]

[QUOTE=Madpoo;506188]Okay, if I understand the drill this time, I marked that in the database as the cofactor being proven prime. It won't show up in the ECM progress report anymore as needing more curves. :smile:[/QUOTE]

Certification of primality is only feasible for exponents up to around 80k.

Even if a cofactor is merely PRP, it still makes no sense to look for any further factors.

The 327th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M3089[/M].

The most recent factor was found by James Hintz, and the PRP test on Primenet is still pending, but [URL="http://factordb.com/index.php?query=2%5E3089-1"]FactorDB[/URL] already shows it as FF (fully-factored).

[QUOTE=GP2;508094][URL="http://factordb.com/index.php?query=2%5E3089-1"]FactorDB[/URL] already shows it as FF (fully-factored).[/QUOTE]
And... now proven.

The 328th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M6679[/M].

The most recent (and also first) factor was found by James Hintz, and the PRP test on Primenet was done by Anonymous. The cofactor is already [URL="http://factordb.com/index.php?id=1100000001249511272"]certified prime on FactorDB[/URL].

This is a semiprime, and its exponent p = 3 mod 4.

So this continues the curious empirically observed tendency that exponents of known Mersenne primes are predominantly 1 mod 4 but exponents of known Mersenne semiprimes are predominantly 3 mod 4. And for Wagstaff primes and Wagstaff semiprimes, the tendency is the opposite.

[QUOTE=GP2;508760]This is a semiprime, and its exponent p = 3 mod 4.[/QUOTE]

It is also p = 7 mod 8.

Among Mersenne semiprimes that are sufficiently large (say, p > 1000) or sufficiently asymmetric (say, the smaller factor has bit length less than 5 percent of the overall bit length), there is an empirically observed tendency that the 3 mod 4 exponents are predominantly 7 mod 8 rather than 3 mod 8. However, the statistics are probably too small to be significant. Applying the same filtering produces the opposite tendency in Wagstaff semiprimes.

See for instance [URL="https://mersenneforum.org/showthread.php?p=503584&postcount=84"]this thread[/URL].

The 329th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M2357[/M].

The 62-digit factor was found by Ryan Propper, and the PRP test on Primenet was done by matzetoni. The cofactor will no doubt soon be [URL="http://factordb.com/index.php?id=1100000001282024818"]certified prime on FactorDB[/URL].

This is a semiprime, and its exponent p = 1 mod 4.