Where is 'M45'? -poll 1

[henryzz]

Originally Posted by davieddy

Each million increase in exponent demands~21,000 tests.
GIMPS completes about 10 tests an hour.

is that 10 tests an hour changing though or is it expected to change because it could take several years for some of these guesses to be reached

[Spherical Cow]

Originally Posted by davieddy

Each million increase in exponent demands~21,000 tests.
GIMPS completes about 10 tests an hour.

Whew- Thanks. So ballpark, it takes almost 90 days to advance a million, and given that we're in the vicinity of 43 million now, we won't see that 56 million boundary for a little over 3 years, and almost 9 years before we reach the region I voted for (79+ million). Wonder what computer I'll be using then...

Norm

[davieddy]

Originally Posted by henryzz

is that 10 tests an hour changing though or is it expected to change because it could take several years for some of these guesses to be reached

10 tests an hour is what I observe currently, but also tallies with
the average over GIMPS 11 years of life. As GIMPS computing clout
increases, so does the computing needed per test.

[henryzz]

Originally Posted by davieddy

10 tests an hour is what I observe currently, but also tallies with
the average over GIMPS 11 years of life. As GIMPS computing clout
increases, so does the computing needed per test.

what i was wondering was are they expected to both increase linearly

[Uncwilly]

Originally Posted by Uncwilly

BTW, I think that we should wait for the polle to be 1 week old before starting the second poll.

Last chance, the poll will be ended and the new started around 7:00pm Hawaii time.

[davieddy]

[davieddy]

Originally Posted by Uncwilly

Last chance, the poll will be ended and the new started around 7:00pm Hawaii time.

Since this deadline has passed, I feel at liberty to offer
my comments on the result of the poll.
The probability of no more primes in the first range is very high.
The probability of no primes between 32M and 43M is >80%
The probability of no primes between 43M and 56M is ~50%
The probability of no primes between 56M and 79M is ~40%

Tests are performed in ascending order.



David

[Fusion_power]

Translating, there should be 1.3 primes from now until we reach 79M. Something about that does NOT ring true to me. From recent history, I would think there were either 2 or 3 primes to be found in that range.


DarJones

[davieddy]

Quoting from the GIMPS home page, we expect 1.78 primes
between exponents x and 2x, so GIMPS has been on a very
lucky streak for the last five primes.
The formula used to estimate the expected primes between
exponents e1 and e2 is 2.57*ln(e2/e1).
This tallies with the values that used to be found on the
old colourful GIMPS status page (which some of us miss sorely)

David

BTW I assume you naively added 0.2 + 0.5 + 0.6 to get 1.3

[davieddy]

Before LLtesting, we expect 1.78 primes with
exponents between 40M and 80M.
The "Poisson distribution" tells us that the
probability of no primes in this range is~17%.
This tallies with my figures above: 0.8*0.5*0.4 = 0.16

Note that the expected number of primes is not 1 - 0.17.
That gives us the probability of one OR MORE primes.

David

NB we have tested exponents up to 2^25
25*1.78 = 44.5

[davieddy]

It is remarkable how well the % poll results reflect
the actual probabilities for each range.

David