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

The 326th fullyfactored or probablyfullyfactored 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 fullyfactored or probablyfullyfactored 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 fullyfactored or probablyfullyfactored 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%5E30891"]FactorDB[/URL] already shows it as FF (fullyfactored). 
[QUOTE=GP2;508094][URL="http://factordb.com/index.php?query=2%5E30891"]FactorDB[/URL] already shows it as FF (fullyfactored).[/QUOTE]
And... now proven. 
The 328th fullyfactored or probablyfullyfactored 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 fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M2357[/M].
The 62digit 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. 
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