mersenneforum.org Prediction for the next prime
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 2008-01-14, 21:56 #1 paulunderwood     Sep 2002 Database er0rr 7×491 Posts Prediction for the next prime This is a simple statistical prediction for the next 3*2^n-1 prime based on historical evidence. It assumes no primes have been missed. The statistics do not take into account the "prime number theorem" Please criticize. Code: "n" Increase over the previous exponent ---- ------------------------------------- 1 0.0000000 2 2.0000000 3 1.5000000 4 1.3333333 6 1.5000000 7 1.1666667 11 1.5714286 18 1.6363636 34 1.8888889 38 1.1176471 43 1.1315789 55 1.2790698 64 1.1636364 76 1.1875000 94 1.2368421 103 1.0957447 143 1.3883495 206 1.4405594 216 1.0485437 306 1.4166667 324 1.0588235 391 1.2067901 458 1.1713555 470 1.0262009 827 1.7595745 1274 1.5405079 3276 2.5714286 4204 1.2832723 5134 1.2212179 7559 1.4723413 12676 1.6769414 14898 1.1752919 18123 1.2164720 18819 1.0384042 25690 1.3651097 26459 1.0299338 41628 1.5733021 51387 1.2344336 71783 1.3969097 81330 1.1329981 85687 1.0535719 88171 1.0289892 97063 1.1008495 123630 1.2737088 155930 1.2612634 164987 1.0580838 234760 1.4229000 414840 1.7670813 584995 1.4101702 702038 1.2000752 727699 1.0365522 992700 1.3641629 1201046 1.2098781 1232255 1.0259848 2312734 1.8768307 3136255 1.3560812 ------------------------ av 1.3400057 std.dev 0.2971180 std.error 0.04 -95% 1.26 3948985.29 +95% 1.42 4456213.62 
 2008-01-15, 00:51 #2 axn     Jun 2003 22·11·107 Posts And what is the probability that no primes would be found between now and 4456213.62? EDIT:- What happens if you take Geometric Mean (or use log of the ratios?) Last fiddled with by axn on 2008-01-15 at 00:52
2008-01-15, 05:29   #3
paulunderwood

Sep 2002
Database er0rr

D6D16 Posts

Quote:
 Originally Posted by axn1 And what is the probability that no primes would be found between now and 4456213.62? EDIT:- What happens if you take Geometric Mean (or use log of the ratios?)
Statistics was not my strong subject.

The geometric mean is 1.31.

My original assumption is based on a standard error for a normal distribution, which it is not the distribution of this data. Here is a stem and leaf diagram betrig:

Code:
1.0   9,4,5,2,3,2,5,2,5,3,2
1.1   6,1,3,6,8,7,7,3,0,0
1.2   7,3,0,8,2,1,3,7,6,0
1.3   3,8,6,9,6,5
1.4   4,1,7,2,1
1.5   0,0,7,4,7
1.6   3,7
1.7   5,6
1.8   8,7
1.9
2.0   0
2.1
2.2
2.3
2.4
2.5   7
More criticism welcome, along with possible answers to anx1's questions.

2008-05-25, 07:37   #4
gd_barnes

May 2007
Kansas; USA

11·929 Posts

Quote:
 Originally Posted by paulunderwood This is a simple statistical prediction for the next 3*2^n-1 prime based on historical evidence. It assumes no primes have been missed. The statistics do not take into account the "prime number theorem" Please criticize.
The NPLB project double-checked k=3 from n=100K-260K and checked it against the k<300 Rieselprime.org page a few months ago. No missing or incorrect primes were found. You're probably aware that Prof. Caldwell and some coharts had already double-checked all k<300 up to n=100K several years ago so now all k=3 for n<260K has been double-checked.

In checking that list vs. your list, I see a typo. Your prime at n=81330 should be n=80330, which would also affect 2 of your ratios. Other then that, your list should be absolutely correct up to n=260K.

NPLB plans to double-check all k=3-1001 up to n=260K by late 2009. So far, we have completed all k=3-25 and 401-417.

Gary

 2008-05-25, 12:05 #5 paulunderwood     Sep 2002 Database er0rr 7×491 Posts A well spotted typo, Gary. The typo only appears in the spreadsheet and makes little difference to the crude calculation. Last fiddled with by paulunderwood on 2008-05-25 at 12:06
2008-05-25, 17:31   #6
gd_barnes

May 2007
Kansas; USA

11×929 Posts

Quote:
 Originally Posted by paulunderwood A well spotted typo, Gary. The typo only appears in the spreadsheet and makes little difference to the crude calculation.
Agreed since you're mostly dealing with the geometric mean. It likely would have a small 'normalizing' effect on the standard error from normal distribution but inconsequential.

 2008-06-16, 20:41 #7 paulunderwood     Sep 2002 Database er0rr 7×491 Posts Here is the latest "crude method" for predicting the next prime based on the last prime. Any modifications such a possion distribution or criticisms are welcome Code: 1 0.0000000 2 2.0000000 3 1.5000000 4 1.3333333 6 1.5000000 7 1.1666667 11 1.5714286 18 1.6363636 34 1.8888889 38 1.1176471 43 1.1315789 55 1.2790698 64 1.1636364 76 1.1875000 94 1.2368421 103 1.0957447 143 1.3883495 206 1.4405594 216 1.0485437 306 1.4166667 324 1.0588235 391 1.2067901 458 1.1713555 470 1.0262009 827 1.7595745 1274 1.5405079 3276 2.5714286 4204 1.2832723 5134 1.2212179 7559 1.4723413 12676 1.6769414 14898 1.1752919 18123 1.2164720 18819 1.0384042 25690 1.3651097 26459 1.0299338 41628 1.5733021 51387 1.2344336 71783 1.3969097 80330 1.1190672 85687 1.0666874 88171 1.0289892 97063 1.1008495 123630 1.2737088 155930 1.2612634 164987 1.0580838 234760 1.4229000 414840 1.7670813 584995 1.4101702 702038 1.2000752 727699 1.0365522 992700 1.3641629 1201046 1.2098781 1232255 1.0259848 2312734 1.8768307 3136255 1.3560812 4235414 1.3504686 av 1.3401779 std.dev 0.2943653 std.error 0.04 -95% 1.26 5342998.07 95% 1.42 6009418.75 mean ānā 5676208.41
2008-06-20, 10:31   #8
davieddy

"Lucan"
Dec 2006
England

6,451 Posts

Quote:
 Originally Posted by axn1 And what is the probability that no primes would be found between now and 4456213.62? EDIT:- What happens if you take Geometric Mean (or use log of the ratios?)
This is analogous to Mersenne primes: a plot of log(n) against
the rank order of each prime fits a straight line well.
We conjecture from this that the expected number of primes between
n1 and n2 is c*ln(n2/n1).
If we take n2/n1 to be your average ratio, we choose c such that
the expected number of primes is one.
We can use this to construct a poll where the ranges represent
the 25% percentiles. The four ranges offered in the poll are:
n<a
a<=n<b
b<=n<c
c<=n
The "fair" choice of ranges has a
75% chance of no primes before a
50% chance of no primes before b
25% chance of no primes before c

The construction of this fair poll (or one with more options)
gives the clearest possible answer to "where is the next prime" IMO.

David

Last fiddled with by davieddy on 2008-06-20 at 11:06

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