Number of octoproths per n

[robert44444uk]

No, you guys are totally right, and I was totally wrong. I did not notice until this morning as I set my computer on its merry way for what I thought was the last 0.6E15, and realised I was a whole magitude adrift.

But I doubt I have the computer resources to run this much further. Each 1E15 takes about 8 hours, so the whole exercise will take someone 10 days.

I will complete to 4E15, and then release this one.

Regards

Robert Smith

[Greenbank]

Originally Posted by robert44444uk

No, you guys are totally right, and I was totally wrong. I did not notice until this morning as I set my computer on its merry way for what I thought was the last 0.6E15, and realised I was a whole magitude adrift.

But I doubt I have the computer resources to run this much further. Each 1E15 takes about 8 hours, so the whole exercise will take someone 10 days.

I will complete to 4E15, and then release this one.

Regards

Robert Smith

If I put my whole G5 on it I can have n=55 done in a shade under 2 days. I think this may be the limit of computing all Octoproths for a specific n. Let me check Robert's estimation formula:-

est(54) = 225950 (actual = 230143)
est(55) = 772429
est(56) = 280214
est(57) = 1253015
est(58) = 2335233
est(59) = 2922982
est(60) = 5869985

I might do n=56 as well, since it has fewer Octoproths than n=55. n=57 looks like a step too far.

[Greenbank]

Originally Posted by Greenbank

est(54) = 225950 (actual = 230143)
est(55) = 772429
est(56) = 280214
est(57) = 1253015

I might do n=56 as well, since it has fewer Octoproths than n=55. n=57 looks like a step too far.

n=55 [0,1E16] = 229947
n=55 [1E16,2E16] = 214250
n=55 [2E16,3E16] = 211102
n=55 [3E16,3.61E16] = 131672

Every 3-prp output by your program was indeed a prime! None failed the tests with PARI.

229947 + 214250 + 211102 + 131672 = 786971

est(54) = 225950 (actual = 230143)
est(55) = 772429 (actual = 786971)

[Greenbank]

OK, n=56 is complete!

Estimate was 280214.

Final count after isprime() PARI checking script: 285415

2^n = 72057594037927936 so I used a kmax of 72060T.

Output:

n=56, kmin=0T, kmax=72060T, version=5.0, here T=10^12
Starting the sieve...
Using the first 11 primes to reduce the size of the sieve array

[285415 lines removed]

The sieving is complete.
Number of Prp tests=1503700301
Time=187990 sec.

So that's 2 days, 4 hours, 13 minutes, 10 seconds.

That's the end of it, not going to start n=57, there are too many of them!

[R. Gerbicz]

Originally Posted by Greenbank

OK, n=56 is complete!
Estimate was 280214.
Final count after isprime() PARI checking script: 285415

That's great!

g(n)=round(f(n)*(1+1/n))

I don't know why but it seems a better formula for large n values! Try it.