[QUOTE=ATH;423033][url]http://www.forbes.com/sites/kevinknudson/2016/01/19/new-record-prime-number-discovered/[/url]



That is nice to know :smile: We are almost certain to find one between 57M and 74M.[/QUOTE]

Is there a prime between 57M and 74M, absolutely.

A mersenne prime? That is a different question

[QUOTE=ewmayer;422993]...
The decimal expansion also contains the exponents of the following known M-primes with p > 100000: 57885161 (once), 37156667 (once), 25964951 (once), 6972593 (3x), 3021377 (4x), 2976221 (3x), 1257787 (2x), 859433 (21x), 756839 (19x), 216091 (28x), 132049 (19x), 110503 (25x). Any p > 100000 not listed does not occur, including the as-yet-unannounced new one.[/QUOTE]

The perfect # for M74207281 contains "74207281" itself, around 74% of the way in.

Would that be considered a mathematical selfie?

[QUOTE=airsquirrels;423034]Is there a prime between 57M and 74M, absolutely.

A mersenne prime? That is a different question[/QUOTE]

I still maintain there's a decent* chance of a lurking prime between 35M and 57M, just waiting for double-checks to discover. :smile:

[SIZE="1"]* By "decent" I merely mean non-negligible.[/SIZE]

I did wonder if having the smallest available exponents actually decreases your chances of finding a prime these days because of the ever-increasing gap between consecutive Mersenne primes, so it's nice to know that there may be a prime in this range (and possibly one missed between 43M and 57M due to a miscalculated residue).

[QUOTE=ATH;423033]
That is nice to know :smile: We are almost certain to find one between 57M and 74M.[/QUOTE]
Sure*, there are about n/ln(n) primes up to n, so there are about M49/ln(M49)-M48/ln(M48) primes in between. Which is not just "few millions", or "few billions", but many more. Unfortunately we won't discover any of them soon, unless double-mersenne project finds a factor of MM48 (which will be in between).

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*note that the article does not say primes between 57M and 74M, we know them all, and it also does not say [U]mersenne[/U] prime between M48 and M49. It just says "primes between M48 and M49, and those are more that atoms in the visible universe. More than atoms in M48 visible universes. And if we are lucky, the double-merseene project can find one.

[QUOTE=Madpoo;423036]I still maintain there's a decent* chance of a lurking prime between 35M and 57M, just waiting for double-checks to discover. :smile:

[SIZE="1"]* By "decent" I merely mean non-negligible.[/SIZE][/QUOTE]

I agree, I've been devoting lots of effort to DC in that range for exactly that reason. Someone has to find the first 'missed' prime

[QUOTE=ATH;423033][URL]http://www.forbes.com/sites/kevinknudson/2016/01/19/new-record-prime-number-discovered/[/URL]

That is nice to know :smile: We are almost certain to find one between 57M and 74M.[/QUOTE]

"We are almost certain" does not mean anything, not to mention the definition of "we". However, it will be quite embarrassing or at least funny if there is another mersenne prime in this range. I am almost certain that we are not certain if the statement is false :-).

[QUOTE][B]Countdown to first time checking all exponents below M(74207281): 81,874[/B][/QUOTE]

Let's guess when we reach this milestone, I'm sure Madpoo or chalsall can make the most educated guesses.

My guess is June 2018, but it might be optimistic. Hopefully the new assignment rules will prevent slow computers holding up the last ones.


[QUOTE=bloodIce;423040]"We are almost certain" does not mean anything, not to mention the definition of "we". However, it will be quite embarrassing or at least funny if there is another mersenne prime in this range. I am almost certain that we are not certain if the statement is false :-).[/QUOTE]

"Almost certain" in a everyday non-mathematical use would be at least above 75% chance imo, maybe higher.

[QUOTE] It is [B][I][STRIKE]almost[/STRIKE] certain[/I][/B] that there are other primes between the old record and this new one, but finding them will take a lot of [STRIKE][B][I]work[/I][/B][/STRIKE] [B][I]luck[/I][/B]. [/QUOTE]
Fixed that. See my post a little bit above. Argument ended. :razz:

Is there any other prime of a special form, which could be tested for a similar time as the most mersennes in the current wave? Just curiosity, if there is a chance that a non-mersenne prime will hold a record ever.

[QUOTE=ATH;423041]My guess is June 2018, but it might be optimistic. Hopefully the new assignment rules will prevent slow computers holding up the last ones.[/QUOTE]

A guestimate based on current heuristics would be approximately 414 days out, or March 8th, 2017.