New milestone

[Primeinator]

Countdown to testing all exponents below M(30402457) once: 111

What do you think...is there a hiding Mersenne in there somewhere?

[TimSorbet]

Originally Posted by Primeinator

Countdown to testing all exponents below M(30402457) once: 111

What do you think...is there a hiding Mersenne in there somewhere?

Seriously doubt it. (duh!) A prime hiding in this one seems more likely, but still quite a longshot:

Countdown to proving M(30402457) is the 43rd Mersenne Prime: 180,214

(I'm just guessing, someone can work the math if they want to check the real odds of each)

[ckdo]

Originally Posted by ckdo

Countdown to proving M(20996011) is the 40th Mersenne Prime: 800

That's another 9 days for another 100 exponents...

Earlier today:

Countdown to proving M(20996011) is the 40th Mersenne Prime: 700

Once again, 9 days for 100 exponents...

[TimSorbet]

Originally Posted by ckdo

Earlier today:

Countdown to proving M(20996011) is the 40th Mersenne Prime: 700

Once again, 9 days for 100 exponents...

Countdown to proving M(20996011) is the 40th Mersenne Prime: 600

11 days for 100 exponents this time.

[ckdo]

Originally Posted by Mini-Geek

Countdown to proving M(20996011) is the 40th Mersenne Prime: 600

11 days for 100 exponents this time.

Countdown to proving M(20996011) is the 40th Mersenne Prime: 500

14 days for the last 100 exponents.

[cheesehead]

A wee Scottie dog canna be expected to run so fast always.

[davieddy]

Originally Posted by Mini-Geek

Seriously doubt it. (duh!) A prime hiding in this one seems more likely, but still quite a longshot:

(I'm just guessing, someone can work the math if they want to check the real odds of each)

We expect(ed!) one Mprime between 20M and 30M.
About 200,000 exponents are not factored.
So the probability of a specified first time LLtest yielding a
prime is 1/200,000.

40,000 have been doublechecked, leaving 160,000
to be doublechecked. Assuming the error rate of tests
is 2%, we get a probability of 1.6% for doublechecking
yielding a prime with exponent<30M.

This agrees with the "expected new primes" shown here:
http://v5www.mersenne.org/report_classic/

David

[Primeinator]

Originally Posted by davieddy

We expect(ed!) one Mprime between 20M and 30M.
About 200,000 exponents are not factored.
So the probability of a specified first time LLtest yielding a
prime is 1/200,000.

40,000 have been doublechecked, leaving 160,000
to be doublechecked. Assuming the error rate of tests
is 2%, we get a probability of 1.6% for doublechecking
yielding a prime with exponent<30M.

This agrees with the "expected new primes" shown here:
http://v5www.mersenne.org/report_classic/

David

We can also consider the fact that we have found an inordinately large number of Mersenne primes close together, inordinately meaning "more than expected." Whether this is an anomaly that is erased by the average in the long run or whether this is a new norm (or anomaly that will continue for at least awhile) remains to be seen.

[davieddy]

Originally Posted by Primeinator

We can also consider the fact that we have found an inordinately large number of Mersenne primes close together, inordinately meaning "more than expected." Whether this is an anomaly that is erased by the average in the long run or whether this is a new norm (or anomaly that will continue for at least awhile) remains to be seen.

The "freakishness" of 8 Mersenne primes in an exponent interval
was discussed in the "Success?..." thread. This is post #346:

Originally Posted by R. Gerbicz

I think it is better to do simulation, using http://primes.utm.edu/notes/faq/NextMersenne.html conjecture for the probability that Mp is prime. 2000 simulations for the [2,5*10^7] interval, gives:

The most number of Mersenne primes in a [x,2.06*x] interval (for the exponent),
 what we have after the verification for M40-M47 are 8 primes.
3 Mersenne primes in 'small' interval: 5
4 Mersenne primes in 'small' interval: 110
5 Mersenne primes in 'small' interval: 536
6 Mersenne primes in 'small' interval: 710
7 Mersenne primes in 'small' interval: 432
8 Mersenne primes in 'small' interval: 162
9 Mersenne primes in 'small' interval: 40
10 Mersenne primes in 'small' interval: 5

So it isn't very rare 8 or more primes, the probability is 10.35%, close to the easy Poission estimation.
.....

Note that the ratio of 2.06 was carefully chosen to be
just greater than log(M47)/log(M40).
Had he chosen a ratio just less than log(M47)/log(M39)
the frequency would be considerably larger.
Ditto if he chose a ratio just less than log(M47)/log(M40)
and looked at the frequency of 7 or more primes, which from
his data is 30%.

Considering that this is the most anomalous feature we can
find, I don't think there is any need to suggest that the
Wagstaff conjecture has come to grief.

David

[ckdo]

Originally Posted by ckdo

Countdown to proving M(20996011) is the 40th Mersenne Prime: 500

14 days for the last 100 exponents.

While I was out ...

Countdown to proving M(20996011) is the 40th Mersenne Prime: 400

20 days for 100 exponents this time...

[henryzz]

Originally Posted by ckdo

While I was out ...

Countdown to proving M(20996011) is the 40th Mersenne Prime: 400

20 days for 100 exponents this time...

i wouldnt be surprised if it doesnt reach 0 before the end of the year(140 days away)