mersenneforum.org Sieve needed for a^(2^b)+(a+1)^(2^b)
 Register FAQ Search Today's Posts Mark Forums Read

2009-06-12, 07:23   #45
robert44444uk

Jun 2003
Suva, Fiji

23×3×5×17 Posts

Quote:
 Originally Posted by R.D. Silverman Question. Singular.
Q1: A more interesting question is whether there exists values of a for
which there are no primes.

Q2: If so, what is the density of that set?

That is a prime number of questions.

Quote:
 Originally Posted by R.D. Silverman The distribution of primes is an interesting topic of research.
Ok, but why isn't the density of primes, a variable and b fixed, not of equal interest? For series with larger b the absolute size of values in the series grows very quickly and its prime probability decreases rapidly.

For b=0, It is possible to demonstrate that the number of primes in the series is infinite. Values are 2a+1, and Dirichlet's AP theory nails that.

A question is whether other values b produce an infinite number of primes. Open question, I would imagine.

One can imagine that at some value of b, there is more than the chance that the number of primes becomes finite, and that, for very large b there are values that do not produce primes - possibly not provable.

2009-06-12, 12:38   #46
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

22·1,877 Posts

Quote:
 Originally Posted by robert44444uk Q1: A more interesting question is whether there exists values of a for which there are no primes. Q2: If so, what is the density of that set? That is a prime number of questions. Ok, but why isn't the density of primes, a variable and b fixed, not of equal interest? .

Because it is ALREADY a known, open problem. Look up
Schinzel's Conjecture and the Bateman-Horn conjecture.

The exact answer to this latter question is well known, but a formal
proof is lacking (for much the same reason as we have no formal proof
of the twin-prime conjecture).

2009-06-14, 05:38   #47
robert44444uk

Jun 2003
Suva, Fiji

23×3×5×17 Posts

Quote:
 Originally Posted by R.D. Silverman Because it is ALREADY a known, open problem. Look up Schinzel's Conjecture and the Bateman-Horn conjecture. The exact answer to this latter question is well known, but a formal proof is lacking (for much the same reason as we have no formal proof of the twin-prime conjecture).
Mmmm, very interesting. Thank you Bob

 2009-06-19, 06:38 #48 robert44444uk     Jun 2003 Suva, Fiji 23·3·5·17 Posts Geoff What is the maximum value that a can take in your program? I was hoping to look at exponent b=10 and I need to start a at 10^10 in order to get 10000 digit prps. But it is telling me I am out of range.
 2009-06-22, 11:21 #49 robert44444uk     Jun 2003 Suva, Fiji 7F816 Posts I would like to reserve b=11, i.e. exponent is 2^11=2048. I have already sieved quite deeply and have already found 16 prps that are 10000 digits or more, and these have been submitted to the Lifchitz site. The first few a's (smaller than 10000 digits) are: Code: a digits 754 5894 1289 6371 1368 6424 3159 7168 3280 7201 3301 7207 4976 7572 6204 7768 6283 7780 6723 7839 6904 7863 7141 7893 10246 8214 11417 8311 13268 8444 Last fiddled with by robert44444uk on 2009-06-22 at 11:25
2009-06-25, 02:36   #50
geoff

Mar 2003
New Zealand

22058 Posts

Quote:
 Originally Posted by robert44444uk Geoff What is the maximum value that a can take in your program? I was hoping to look at exponent b=10 and I need to start a at 10^10 in order to get 10000 digit prps. But it is telling me I am out of range.
a is limited to about 2^31. I could increase that to 2^62 if necessary.

2009-06-26, 05:44   #51
robert44444uk

Jun 2003
Suva, Fiji

23×3×5×17 Posts

Quote:
 Originally Posted by geoff a is limited to about 2^31. I could increase that to 2^62 if necessary.
That would be great Geoff.

I tested b=11 up to a=100000 and I am well on the way to a=200000.

Results for first 100000:

Average prp size = 9250 digits. Digits at a=50000, 9624

Expected number of prps in population of 100000 odd numbers at that digits length:
100000/2*ln(10^9250)= 9.38; 100000/2*(ln(10^9624)= 9.02

prps found: 79

 2009-06-27, 15:20 #52 robert44444uk     Jun 2003 Suva, Fiji 111111110002 Posts Results up to a=200000, 72 of which are of interest to the Lifchitz prp site. Code: prp, no of digits 754^2048+755^2048,5895 1289^2048+1290^2048,6371 1368^2048+1369^2048,6424 3159^2048+3160^2048,7168 3280^2048+3281^2048,7201 3301^2048+3302^2048,7207 4976^2048+4977^2048,7572 6204^2048+6205^2048,7768 6283^2048+6284^2048,7780 6723^2048+6724^2048,7839 6904^2048+6905^2048,7863 7141^2048+7142^2048,7893 10246^2048+10247^2048,8214 11417^2048+11418^2048,8311 13268^2048+13269^2048,8444 15456^2048+15457^2048,8580 19428^2048+19429^2048,8784 19683^2048+19684^2048,8795 19698^2048+19699^2048,8796 20298^2048+20299^2048,8822 21484^2048+21485^2048,8873 22543^2048+22544^2048,8916 23702^2048+23703^2048,8960 23815^2048+23816^2048,8965 24747^2048+24748^2048,8999 27010^2048+27011^2048,9077 32319^2048+32320^2048,9236 34133^2048+34134^2048,9285 36201^2048+36202^2048,9337 37030^2048+37031^2048,9357 39438^2048+39439^2048,9413 41292^2048+41293^2048,9454 44472^2048+44473^2048,9520 47623^2048+47624^2048,9580 50198^2048+50199^2048,9628 51031^2048+51032^2048,9642 51370^2048+51371^2048,9648 51521^2048+51522^2048,9651 52628^2048+52629^2048,9670 53073^2048+53074^2048,9677 53309^2048+53310^2048,9681 53767^2048+53768^2048,9689 55911^2048+55912^2048,9724 56630^2048+56631^2048,9735 59424^2048+59425^2048,9778 59583^2048+59584^2048,9780 61797^2048+61798^2048,9813 61930^2048+61931^2048,9815 63346^2048+63347^2048,9835 64551^2048+64552^2048,9851 66076^2048+66077^2048,9872 66396^2048+66397^2048,9877 66674^2048+66675^2048,9880 67392^2048+67393^2048,9890 67704^2048+67705^2048,9894 68934^2048+68935^2048,9910 69349^2048+69350^2048,9915 69521^2048+69522^2048,9917 70510^2048+70511^2048,9930 70583^2048+70584^2048,9931 70601^2048+70602^2048,9931 71168^2048+71169^2048,9938 72189^2048+72190^2048,9951 75127^2048+75128^2048,9986 76974^2048+76975^2048,10008 77074^2048+77075^2048,10009 78493^2048+78494^2048,10025 81114^2048+81115^2048,10055 81544^2048+81545^2048,10059 83794^2048+83795^2048,10084 83896^2048+83897^2048,10085 88373^2048+88374^2048,10131 88830^2048+88831^2048,10135 89768^2048+89769^2048,10145 91595^2048+91596^2048,10163 93534^2048+93535^2048,10181 93782^2048+93783^2048,10184 94243^2048+94244^2048,10188 95891^2048+95892^2048,10202 100757^2048+100758^2048,10248 101197^2048+101198^2048,10251 103577^2048+103578^2048,10272 112746^2048+112747^2048,10348 114562^2048+114563^2048,10362 115780^2048+115781^2048,10371 119216^2048+119217^2048,10396 119791^2048+119792^2048,10401 120264^2048+120265^2048,10405 121334^2048+121335^2048,10413 122038^2048+122039^2048,10418 122543^2048+122544^2048,10422 122927^2048+122928^2048,10424 127699^2048+127700^2048,10458 132663^2048+132664^2048,10492 134315^2048+134316^2048,10503 135212^2048+135213^2048,10509 136141^2048+136142^2048,10515 136907^2048+136908^2048,10520 139844^2048+139845^2048,10539 141774^2048+141775^2048,10551 143390^2048+143391^2048,10561 143774^2048+143775^2048,10564 143878^2048+143879^2048,10564 147617^2048+147618^2048,10587 147696^2048+147697^2048,10588 149603^2048+149604^2048,10599 149622^2048+149623^2048,10599 150635^2048+150636^2048,10605 152562^2048+152563^2048,10617 153794^2048+153795^2048,10624 154919^2048+154920^2048,10630 155382^2048+155383^2048,10633 156064^2048+156065^2048,10637 158330^2048+158331^2048,10650 159409^2048+159410^2048,10656 159450^2048+159451^2048,10656 160497^2048+160498^2048,10662 163585^2048+163586^2048,10679 164367^2048+164368^2048,10683 164376^2048+164377^2048,10683 166566^2048+166567^2048,10695 168247^2048+168248^2048,10704 168501^2048+168502^2048,10705 169670^2048+169671^2048,10711 174775^2048+174776^2048,10737 179939^2048+179940^2048,10763 181393^2048+181394^2048,10769 182116^2048+182117^2048,10774 182749^2048+182750^2048,10777 183451^2048+183452^2048,10780 184125^2048+184126^2048,10784 184607^2048+184608^2048,10786 185491^2048+185492^2048,10790 186829^2048+186830^2048,10797 194559^2048+194560^2048,10833 195325^2048+195326^2048,10836
 2009-07-15, 21:43 #53 geoff     Mar 2003 New Zealand 13·89 Posts I have uploaded a new version of the sieve 0.2 that allows a up to 2^62-2. It will use a bit more memory and might be a bit slower than the previous version. I haven't tested it at all, so let me know if there are any problems.
2009-07-26, 07:13   #54
robert44444uk

Jun 2003
Suva, Fiji

23·3·5·17 Posts

Quote:
 Originally Posted by henryzz i accidentally left b=12 running quite a lot longer than i meant to and found: 311^(2^12)+312^(2^12) 2741^(2^12)+2742^(2^12) 3582^(2^12)+3583^(2^12) 5293^(2^12)+5294^(2^12) are all 3-prp i expect they are already known
Henryzz, are you still running this or is this 2^12 now free? What was the highest value you checked? I might carry on from where you left off if you are done.

Last fiddled with by robert44444uk on 2009-07-26 at 07:14

2009-07-29, 09:08   #55
henryzz
Just call me Henry

"David"
Sep 2007
Liverpool (GMT/BST)

37×163 Posts

Quote:
 Originally Posted by robert44444uk Henryzz, are you still running this or is this 2^12 now free? What was the highest value you checked? I might carry on from where you left off if you are done.
i only ran this for a couple a days
i only meant to run for a few hours as a test but i forgot to stop it
i have not a clue where i searched up to

 Similar Threads Thread Thread Starter Forum Replies Last Post pinhodecarlos NFS@Home 46 2018-03-12 22:43 binu Factoring 3 2013-04-13 16:32 beyastard Software 55 2009-07-29 12:51 AntonVrba Math 3 2007-03-06 10:55 MooooMoo Twin Prime Search 9 2007-01-01 21:13

All times are UTC. The time now is 19:14.

Sat Feb 4 19:14:47 UTC 2023 up 170 days, 16:43, 1 user, load averages: 0.82, 0.76, 0.84