[URL="http://www.theguardian.com/science/alexs-adventures-in-numberland/2016/jan/19/largest-prime-number-yet-discovered-has-22-million-digits"]The Guardian[/URL] :smile:

[QUOTE=Dubslow;423001]I was using the search function in my text editor, in which I had opened the "official" file hosted on mersenne.org, which has newlines every 100 chars... and the first instance of e that you listed starts two chars before a newline. My pi statistic may well be false too.

I can't even spill the beans correctly.[/QUOTE]

As long as you spill them voluminously, or something. :)

I use my own code to generate the decimal printouts - still way slower than it could be, took ~3 hours on 1 cpu of my 2GHz Core2Duo macbook classic, probably at least 100x slower than it could be, but we do these so rarely it's low on my coding priority list - and switched from the original 100-column-wrapped (useful for debugging by way of comparing vs the official files of these) to no-linefeed form both for this reason, and for the fact that the resulting files have byte counts exactly reflecting the number of digits in the number in question.

[QUOTE=ewmayer;423144]As long as you spill them voluminously, or something. :)

I use my own code to generate the decimal printouts - still way slower than it could be, took ~3 hours on 1 cpu of my 2GHz Core2Duo macbook classic, probably at least 100x slower than it could be, but we do these so rarely it's low on my coding priority list - and switched from the original 100-column-wrapped (useful for debugging by way of comparing vs the official files of these) to no-linefeed form both for this reason, and for the fact that the resulting files have byte counts exactly reflecting the number of digits in the number in question.[/QUOTE]

For the website, I used yafu to spit out the digits (and for the perfect # as well), then used a handy little app "tpipe" to add the line feeds at 100 columns. Oh, and yafu only took < 1 minute on my puny laptop...it's fast.

Why 100 columns? Beats me, but I noticed that M48's files used that, and I'm a slave to tradition?

Truth be told, when I'd load up the unwrapped version in *anything* it would take forever to load it as one long 22 megacharacter line of text. I suspect this wouldn't be unique to me or the apps I use, and it's really just for fun anyway. I suppose anyone looking to do any kind of analysis would simply strip out the cr/lf.

[QUOTE=ramshanker;423072][url]https://news.ycombinator.com/item?id=10931234[/url]

Going steady.[/QUOTE]

Some of the funnier posts from that thread:

o banku_brougham 6 hours ago: [i]So if a mathematical fact is known by one person, "it is known."[/i]

==> dandelany 12 minutes ago: [i]And if it's known by more than one person, it's "trivial" :)[/i]

o gitpusher 4 hours ago: [i]"Meanwhile, somewhere in Wisconsin, the number 274-207-2811 is being mercilessly prank-called by mathematicians."[/i]

[ewm: Actually, all of ...281[0-9] are probably being prank-called ... or perhaps -2811 is the only one where someone picked up.]

[QUOTE=ATH;423075](Btw I did find the factors 7 and 22127627 of the M57885161 perfectnumber + 1, and factors 3593 and 7089208037 for the M42643801 perfectnumber + 1 long ago, I just never got the thread updated).

Can any special form of the factors of M[SUB]p[/SUB]*(M[SUB]p[/SUB]+1)/2 + 1 = 2[SUP]p-1[/SUP]*(2[SUP]p[/SUP] - 1) + 1 = 2[SUP]2p-1[/SUP] - 2[SUP]p-1[/SUP] +1 be deduced?[/QUOTE]
No, but "the perfectnumber - 1" = M[SUB]p[/SUB]*(M[SUB]p[/SUB]+1)/2 - 1 = (M[SUB]p[/SUB]-1)/2 * (M[SUB]p[/SUB]+2) :smile:

[QUOTE=ewmayer;422993]Hmm ... I get 3 occurrences of 2718281, starting at digits ... 19391387. [Those counts treat the most-significant digit as the first and increase rightward, as in "Nth char in a file containing the decimal expansion," as displayed by many text editors in their positioning indicators.][/QUOTE]

I expect that this hint on its own is enough to uniquely identify 74,207,281 in the 74M range. But it still seems rather difficult to me. I wrote some code that makes use of Mpir.NET (GMP fork), but it's too slow for me to want to let it run to completion (~24 CPU hours), even after trying to optimize it a bit by trying to more efficiently calculate those digits instead of just turning the whole Mp number into a string. (checking a single number isn't too bad, but multiply that by 55050 primes in the range and...)

Is there a better way [URL="http://pastebin.com/F7ns2k3k"]than what I did[/URL]? Or did those who found it using this sort of hint just have more patience than I did? (in my own defense, I knew the announcement would come within 3 hours by the time I saw the hints :smile:) Or maybe they used PrimeNet's data to eliminate some possibilities, like the >35000 that had factors.

[QUOTE=ewmayer;423146]Some of the funnier posts from that thread:

o banku_brougham 6 hours ago: [i]So if a mathematical fact is known by one person, "it is known."[/i]

==> dandelany 12 minutes ago: [i]And if it's known by more than one person, it's "trivial" :)[/i]

o gitpusher 4 hours ago: [i]"Meanwhile, somewhere in Wisconsin, the number 274-207-2811 is being mercilessly prank-called by mathematicians."[/i]

[ewm: Actually, all of ...281[0-9] are probably being prank-called ... or perhaps -2811 is the only one where someone picked up.][/QUOTE]

Funny that we should mention phone numbers. When I first saw the exponent this morning, the "207" jumped out at me, as we have a home in Maine, one of the few remaining states with a single statewide area code: 207. The (207) 281-xxxx exchange is Saco, Maine. I wouldn't be surprised if I have dialed numbers in that exchange before, as we frequently have spent the night in and done business with a few companies in that area.

[QUOTE=ewmayer;423144]I use my own code to generate the decimal printouts - still way slower than it could be, took ~3 hours on 1 cpu of my 2GHz Core2Duo macbook classic, probably at least 100x slower than it could be, but we do these so rarely it's low on my coding priority list - ...[/QUOTE]

[QUOTE=Mini-Geek;423149]Is there a better way [URL="http://pastebin.com/F7ns2k3k"]than what I did[/URL]? [/QUOTE]
All the bicycles are invented a long time ago, dudes... :rolleyes:
[CODE]# time ../pfgw64.exe -od -q"2^74207281-1" > M49
PFGW Version 3.7.9.64BIT.20141125.x86_Dev [GWNUM 28.7]

[COLOR=Green]11.364u[/COLOR] 0.220s 0:10.73 107.9% 0+0k 0+43648io 0pf+0w

@ wc M49
1 2 22338669 M49

# cut -c-50 M49
2^74207281-1: 300376418084606182052986098359166050
[/CODE]

Congratulations everyone :smile:

[QUOTE=Mini-Geek;423066]If my calculations are right, we can expect about 0.18 more Mersenne primes in the 57M < p < 75M range. So it's not almost certain that we'll find another Mersenne there, rather it's almost certain (to be precise: ~85% likely) that we'll find no more Mersennes in that range.[/QUOTE]

Using the Lenstra/Pomerance heuristic as described on [url=http://primes.utm.edu/notes/faq/NextMersenne.html]Chris Caldwell's page[/url], I get significantly higher odds:
[i]
Using 906644 odd primes in [57885161,74207281], of which (453233,453411) == 1,3 (mod 4); Expected #Mp with p == 1,3 (mod 4) = 0.351, 0.332
[/i]
Thus summed odds of 0.683.

George, what does your own odds-calculator say?

[b]Edit:[/b] Whoops! I just summed the asymptotic-estimate odds over each prime in the interval ... no accounting for the ones for which TF has found a factor (unsure how to account for that if at all, since the above heuristic is based on TF-style odds) and for ones already have had an LL test. Can someone fill in the fraction [strike]already[/strike]not yet LL-tested and multiply my simple-sum result by it?

[QUOTE=ewmayer;423164]Using the Lenstra/Pomerance heuristic as described on [url=http://primes.utm.edu/notes/faq/NextMersenne.html]Chris Caldwell's page[/url], I get significantly higher odds:
[i]
Using 906644 odd primes in [57885161,74207281], of which (453233,453411) == 1,3 (mod 4); Expected #Mp with p == 1,3 (mod 4) = 0.351, 0.332
[/i]
Thus summed odds of 0.683.

George, what does your own odds-calculator say?

[b]Edit:[/b] Whoops! I just summed the asymptotic-estimate odds over each prime in the interval ... no accounting for the ones for which TF has found a factor (unsure how to account for that if at all, since the above heuristic is based on TF-style odds) and for ones already have had an LL test. Can someone fill in the fraction already LL-tested and multiply my simple-sum result by it?[/QUOTE]

The milestones page shows 81,788 exponents remaining to be first-time checked below M49.

If we further estimate that 5% of the 554,000 that need double-checking below M49 will be bad, that's another ~27,700 that we may as well treat as if they weren't done at all yet.