mersenneforum.org GAPS BETWEEN PRIME PAIRS (Twin Primes)
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 2019-05-16, 09:43 #56 Thomas11     Feb 2003 3×5×127 Posts Please keep in mind that we use an overlap of just 10000. The Perl script also uses this number as array size. That means that gaps larger than 10000 would be lost without further notification! Thus, as soon as you observe gap lengths of 8000 or higher, we need to adjust this number to a higher one (e.g. 15000 or 20000).
 2019-05-16, 10:28 #57 Thomas11     Feb 2003 3×5×127 Posts Just for your information: The "technical" upper limit for the search as dictated by NewPGen would be k=9.2234e18 (equivalent to 5.534e19 in "real" numbers). I did a quick test run at this level (k=9e18) and found the script combo working properly up to this bound.
 2019-05-16, 10:37 #58 Thomas11     Feb 2003 3×5×127 Posts The test run revealed the following new gaps, luckily including one for 3016: Code: 3016 9000000000206619002 3246 9000000000189953452 3270 9000000000039902107 3650 9000000000092227858 3770 9000000000022662393 3865 9000000000125118057 But I suppose all of them would be replaced soon by lower k's.
2019-05-16, 10:54   #59
Thomas11

Feb 2003

35618 Posts

Quote:
 Originally Posted by Thomas11 I did a quick test run at this level (k=9e18) and found the script combo working properly up to this bound.
Ermm, this is only true for the Linux version of the run script.
Actually the limit on Windows would be lower: k=2.147e17 (= 2.147e9 * 1e8) due to the restriction of "kmin" and "kmax" to 32 bit (signed) integers.

But we could cope with this restriction by switching to "units" of 1e10 for kmin and kmax. However, in order to avoid segmented sieving, the step size still needs to be 2e8. This would require a more sophisticated string handling for the loop processing, but should be easy to solve once we need it...

Last fiddled with by Thomas11 on 2019-05-16 at 11:07 Reason: Messed up the differnt powers of 10...

2019-05-16, 14:26   #60
Thomas11

Feb 2003

3·5·127 Posts

Quote:
 Originally Posted by robert44444uk Sorry - my bad. Thomas11 is right about the situation. In his run_new.bat file, you need to set kmin at 9000000 and kmax at say 9500000 I have 14 cores working on this starting at kmin 2333333 up to 8000000
Is the interval between 8000000 and 9000000 still available?
Then I would like to start from 8000000.

 2019-05-16, 14:33 #61 Thomas11     Feb 2003 3·5·127 Posts Three new record gaps from the (current) upper bound of the Windows script: Code: 4275 210000040694249670 4363 210000037721159782 4840 210000040389168323 Let's see how long they would last...
2019-05-16, 15:30   #62
robert44444uk

Jun 2003
Oxford, UK

35238 Posts

Quote:
 Originally Posted by Thomas11 Is the interval between 8000000 and 9000000 still available? Then I would like to start from 8000000.
Sorry I'd already started 8m to 9m. I can adjust this to go from 8m to 8.5m though, so that you could take 8.5m onwards.

I've got to 2138278 and found 7 3000 gaps, but none of these is first instance.

Last fiddled with by robert44444uk on 2019-05-16 at 15:36

2019-05-16, 15:45   #63
Thomas11

Feb 2003

111011100012 Posts

Quote:
 Originally Posted by robert44444uk Sorry I'd already started 8m to 9m. I can adjust this to go from 8m to 8.5m though, so that you could take 8.5m onwards.
Okay, then I'll start from 8.5m.

 2019-05-16, 15:53 #64 Thomas11     Feb 2003 3·5·127 Posts This is a nice one: Code: 3333 865501685832150
2019-05-16, 16:05   #65
robert44444uk

Jun 2003
Oxford, UK

35238 Posts

I'm wondering if for the perl function Math::Prime::Utils sieve_prime_cluster might be a solution to the size problem - also, it can be called from memory rather than from the written newpgen file

https://metacpan.org/pod/Math::Prime..._prime_cluster

Took about 7 secs to spew 2e8 to 4e8 twins to screen.

Quote:
 my @s = sieve_prime_cluster(1, 1e9, 2,6,8,12,18,20); Efficiently finds prime clusters between the first two arguments low and high. The remaining arguments describe the cluster. The cluster values must be even, less than 31 bits, and strictly increasing. Given a cluster set C, the returned values are all primes in the range where p+c is prime for each c in the cluster set C. For returned values under 2^64, all cluster values are definitely prime. Above this range, all cluster values are BPSW probable primes (no counterexamples known). This function returns an array rather than an array reference. Typically the number of returned values is much lower than for other primes functions, so this uses the more convenient array return. This function has an identical signature to the function of the same name in Math::Prime::Util:GMP. The cluster is described as offsets from 0, with the implicit prime at 0. Hence an empty list is asking for all primes (the cluster p+0). A list with the single value 2 will find all twin primes (the cluster where p+0 and p+2 are prime)….

Last fiddled with by robert44444uk on 2019-05-16 at 16:12

 2019-05-17, 01:54 #66 firejuggler     Apr 2010 Over the rainbow 3·11·73 Posts just saying' Code: 4905 9000382149988845 how do I calculate merit? what's the twin prime constant? Last fiddled with by firejuggler on 2019-05-17 at 02:02

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