Isn't a new M. prime overdue?

[retina]

Originally Posted by davar55

I thought we already found one in that range. Does that mean
we only expect 1/3 of another M.prime in 40M-80M? Isn't that
like 2.3 children in the average family? Aren't we dealing with
integers?

I think Mini-Me counts as 0.3 of a person.

[Uncwilly]

Originally Posted by retina

I think Mini-Me counts as 0.3 of a person.

Not 3/5?

[davar55]

Not 3/5?

Mustn't be so intolerant (if I read that right).

[davar55]

We have found 2 in that range.

Which 8 digit M.primes have been found so far?

[science_man_88]

Originally Posted by davar55

Which 8 digit M.primes have been found so far?

Originally Posted by http://en.wikipedia.org/wiki/Mersenne_prime

13,466,917
24,036,583
25,964,951
30,402,457
32,582,657
37,156,667
42,643,801
43,112,609

these are the 8 digit exponents Wikipedia has.

[science_man_88]

Originally Posted by davar55

Which 8 digit M.primes have been found so far?

if you meant by digits in how many digits:

11,185,272
12,837,064
12,978,189

is your list.

[Mini-Geek]

See http://primes.utm.edu/mersenne/ for a list of known Mersenne primes, of course the two known in the 40M-80M range are M42643801 and M43112609. In this range we would have expected 1.78 primes total, but we've already got two and have searched enough to only expect 1.3 more, so we can expect to have found 3.3 primes in the end. And just like the 2.3 children in a family thing, yes, in any specific case, the number of Mersenne primes in an interval will be an integer above or below the average, but on average you can expect however many things to be in each.
It's like flipping a coin, except in our case it's weighted very heavily to the "composite" side. But let's talk about a fair coin that you're flipping 100 times. Clearly, you can expect to get 50 heads and 50 tails. If you've already flipped the first 10, and 8 came up heads, then in the rest you expect 45 heads and 45 tails, (the past results doesn't mean you now expect fewer heads than tails - and you can never expect a negative number of primes in a range) so in total, you expect there to be 53 heads and 47 tails. Similarly, in the first (however many candidates searched) in the 40M-80M range, we've found 2 primes (and many composites). For the rest of it, we still expect 1.3 more primes, because (as far as we know, anyway) future Mersenne primes are not at all determined by past ones, so we can expect 3.3 primes to end up in the 40M-80M range, even though in the end it will be 2, 3, 4, 5, or some higher integer of primes.

[science_man_88]

Does the dsum of the dsum of 2^p-1 and p always come to 1,2,3,5,8 ? I think my data suggest. It might be nice to know.

[science_man_88]

(10:21)>x=0;y=0;for(i=1,#mersenne,y=dsum(2^mersenne[i]-1);x=dsum(mersenne[i]);until(y<10 && x<10,y=dsum(y);x=dsum(x));print1(dsum(x+y)","))
5,1,9,8,5,3,2,5,8,3,3,2,3,5,2,8,5,5,9,5,9,9,3,6,6,8,2,9,2,2,2,6,9,
  *** _%_: user interrupt after 44mn, 9,437 ms.
(10:32)>

I think my PARI timer is broke by the looks of it.Looks like 7 never comes up but I'm not sure.

fixed it with a few gettime() calls by the looks of it.

doh 7 never appears because 9x+3 and 9x+6 are never prime!

[davieddy]

Originally Posted by Mini-Geek

Similarly, in the first (however many candidates searched) in the 40M-80M range, we've found 2 primes (and many composites). For the rest of it, we still expect 1.3 more primes, because (as far as we know, anyway) future Mersenne primes are not at all determined by past ones, so we can expect 3.3 primes to end up in the 40M-80M range, even though in the end it will be 2, 3, 4, 5, or some higher integer of primes.

Good clear post as usual.

Furthermore, the probability (as of now) of 2+x primes in the range
is given by the Poisson distribution:

P(2+x) = e^-1.3 * 1.3^x / x!

x is an integer of course.

(I love the way just one figure (1.3 in this case) can tell you so much,
given the simple assumption Mini-Geek mentioned.)

Another point to note is that factoring doesn't
affect the expected new primes: finding factors
for some candidates increases the probability of
the candidates for which no factor was found being prime.

David

BTW does anyone else agree with me that the
"recent results" page would make more interesting
browsing if the NF category was omitted completely?

[petrw1]

Originally Posted by davieddy

BTW does anyone else agree with me that the
"recent results" page would make more interesting
browsing if the NF category was omitted completely?

I agree....

or ....I recall seeing a similar suggestion a while back; that is to give us the option on this report to exclude NF. The problem with that suggestion though is I believe the report is built at the start of each hour. I suppose an option then would be to create 2 canned reports: 1 with NF and 1 without.

On that topic I'd also ask that since it is run once per hour I'd like to see all results since the last report; knowing some could be much more than 1,000 if there was a bulk of manual assignments turned in.

AND on the topic of that topic I'd like to suggest that the Mods/Gerbils/etc create a Thread under Software with a clear topic like "Suggestion Box" where all suggestions could be collected in 1 place so that George et al would only have to look in this 1 place for suggestions.