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2013-07-29, 14:16   #540
Thomas11

Feb 2003

35738 Posts

Quote:
 Originally Posted by robert44444uk I thought I would plot x=nth prime versus y=ln2(ln2(k*2^n-1)) and see what I got. As expected a very linear relationship and what's more this suggests the 200th prime at about n=475,000 unless I did the maths wrong. Actually, I think it will be greater than this value.
Seems that your estimate was right on the spot!
At least until you will not discover another prime below n=250k.

2013-07-30, 08:28   #541
robert44444uk

Jun 2003
Oxford, UK

201610 Posts

Quote:
 Originally Posted by robert44444uk I thought I would plot x=nth prime versus y=ln2(ln2(k*2^n-1)) and see what I got. As expected a very linear relationship and what's more this suggests the 200th prime at about n=475,000 unless I did the maths wrong.
Gosh, what was I thinking when I typed that formula! I meant:

x=nth prime versus y=log2(log2(k*2^n-1)) where log2 is log base 2.

Starting this morning at n=227953. I should be able to speed up when I get to 230000.

 2013-07-30, 13:01 #542 robert44444uk     Jun 2003 Oxford, UK 7E016 Posts I did some factoring to try to understand why the candidate is so prime. The results are interesting: odd primes <10000 total 1,228 Primes <10000 with modulo2 <1001 total 433 Looking at the 433 primes: A Payam E(130) to which this candidate belongs eliminates 15 primes <10000 where prime p has modulo2 of p-1, and 86 other primes, a total of 101 primes <10000 There are 52 primes >131 and <1000 that are p-1 modulo2 (these cannot be eliminated in a power series base 2) This leaves 280 primes that are modulo 2 <1000 where a Payam number might be more efficient than another Payam number of the same E(130) class. The 280 is equal to 433-101-52 Of the 280 primes, only 74 of those provide factors in the series, an extremely low number. The candidate eliminates a further 206 primes that are <10000 and are <1000 modulo 2. These are shown in the list: Code: prime modulo2 271 135 311 155 313 156 383 191 449 224 487 243 577 144 593 148 599 299 607 303 617 154 647 323 691 230 733 244 739 246 751 375 809 404 811 270 823 411 839 419 863 431 919 153 929 464 971 194 983 491 991 495 997 332 1009 504 1021 340 1049 262 1051 350 1063 531 1097 274 1151 575 1153 288 1193 298 1201 300 1217 152 1223 611 1231 615 1249 156 1279 639 1289 161 1327 221 1361 680 1399 233 1433 179 1459 486 1543 771 1553 194 1567 783 1583 791 1597 532 1601 400 1607 803 1609 201 1627 542 1663 831 1697 848 1699 566 1709 244 1721 215 1753 146 1759 879 1811 362 1831 305 1871 935 1889 472 1933 644 1951 975 1993 996 1999 333 2003 286 2017 336 2129 532 2179 726 2203 734 2251 750 2281 190 2287 381 2341 780 2347 782 2383 397 2393 598 2441 305 2473 618 2657 166 2671 445 2689 224 2749 916 2767 461 2791 465 2917 972 2969 371 3049 762 3061 204 3109 444 3121 156 3137 784 3217 804 3221 644 3271 545 3331 222 3343 557 3361 168 3389 484 3449 431 3457 576 3463 577 3529 882 3541 236 3631 605 3739 534 3761 188 3821 764 3823 637 3833 958 3889 648 3943 219 4001 1000 4049 506 4057 169 4129 688 4153 346 4201 525 4211 842 4271 305 4273 534 4297 537 4409 551 4421 340 4423 737 4519 753 4523 266 4567 761 4643 422 4657 388 4663 777 4721 295 4729 788 4733 364 4751 475 4759 793 4861 972 4871 487 4931 986 4993 624 4999 357 5081 635 5167 861 5209 217 5237 748 5279 377 5297 662 5347 198 5441 544 5471 547 5503 917 5531 790 5569 464 5669 436 5689 711 5711 571 5737 239 5821 388 5867 838 5953 992 6043 318 6089 761 6337 288 6353 397 6449 806 6481 810 6563 386 6679 159 6689 836 6857 857 6871 687 6959 497 7001 500 7057 392 7151 325 7351 525 7393 264 7487 197 7489 468 7753 323 7867 874 7993 999 8161 408 8317 308 8353 464 8581 660 8713 363 8761 365 8831 883 8929 496 9041 904 9413 724 9431 943 9511 317 9521 476 9623 283 9721 810 9781 652 9929 292
 2013-07-30, 14:04 #543 robert44444uk     Jun 2003 Oxford, UK 25×32×7 Posts The lack of small factors clearly has large impact on any sieving. The candidate exhibits the following persistence: Code: Sieve limit candidates remaining 10^4 61.02% 10^5 49.29% 10^6 41.09% 10^7 35.09% 6.34*10^12 19.26% I can't calculate the Nash weight using the software I have.
2013-07-30, 15:56   #544
Thomas11

Feb 2003

35738 Posts

Quote:
 Originally Posted by robert44444uk I can't calculate the Nash weight using the software I have.
Please try the attached program (Windows 32 bit console application).

Usage is a follows:

Code:
Nash_Payam.exe <S/R> <E> <y>
For example:

Code:
Nash_Payam.exe R 130 22544089918041953

R 130 22544089918041953 8818
Attached Files
 Nash_Payam.exe (123.5 KB, 298 views)

 2013-07-30, 16:26 #545 robert44444uk     Jun 2003 Oxford, UK 201610 Posts Hah, there is a surprise. It turns out that the candidate has one of the weakest weights in its class of Riesel E130 Payams that are VPS. A survey of 189 such candidates has a top weight of 9284, a lowest weight of 8565, and a median weight of 8951 compared to the candidates weight of 8818. Thank you for lending me a new toy though, Thomas11, I shall play with this for all of the Riesel VPS As of 17:30 tonight I am up to 228639, and no more prp/primes. I'm still advancing 230-240 and 240-250 on two other consoles. I have checked 199 prp and confirm that they are prime.
 2013-07-30, 17:16 #546 robert44444uk     Jun 2003 Oxford, UK 37408 Posts What lovely toy. I put all of my VPS through it and produced the following: Code: Max Min Median 28 7190 6977 6989 36 7776 6878 7538 52 8405 7117 7799 58 8417 7089 7927.5 60 8661 7572 8087 66 8971 7475 8197 82 8870 7906 8419.5 100 9156 8244 8716 106 9196 8418 8817.5 130 9284 8565 8951 138 9344 8705 9068 148 9394 8915 9152 162 9595 9120 9324 172 9497 9357 9418 178 9527 9322 9447 180 9685 9343 9522.5 196 9651 9649 9650 The game does not work for the supergiants - R268 and R292 both show all at 10000 Last fiddled with by robert44444uk on 2013-07-30 at 17:25
2013-07-30, 17:46   #547
Thomas11

Feb 2003

5×383 Posts

Quote:
 Originally Posted by robert44444uk The game does not work for the supergiants - R268 and R292 both show all at 10000
Sorry, it was limited to E<268.

Please try the attached version. It should work up to E=466 (if ever needed).
Attached Files
 Nash_Payam.exe (123.5 KB, 195 views)

 2013-07-30, 20:04 #548 Thomas11     Feb 2003 5·383 Posts Here is a similar table of the Nash weights for the Sierpinski side: Code: E count Min Max Average --------------------------------------- 28 6 6966 7579 7324.7 36 0 -- -- -- 52 3206 6845 8409 7809.6 58 3296 7161 8603 7939.6 60 2938 7259 8819 8059.4 66 3135 7350 8836 8186.9 82 3316 7834 8999 8423.3 100 1369 8067 9164 8710.7 106 897 8376 9224 8817.9 130 856 8562 9312 8949.1 138 646 8680 9404 9067.5 148 246 8827 9536 9157.3 162 42 9108 9525 9315.4 172 47 9108 9574 9389.6 178 36 9318 9663 9457.9 180 42 9285 9734 9520.9 196 5 9608 9869 9748.2 210 4 9613 9788 9703 226 1 9794 9794 9794 --------------------------------------- Total: 20088 Note the similarities of the average weights for Riesel and Sierpinski side! Last fiddled with by Thomas11 on 2013-07-30 at 20:16
 2013-07-31, 07:51 #549 Thomas11     Feb 2003 5×383 Posts Let's start the day with another prime: 202? 496187
2013-07-31, 09:11   #550
robert44444uk

Jun 2003
Oxford, UK

7E016 Posts

Quote:
 Originally Posted by Thomas11 Let's start the day with another prime: 202? 496187
The way one does! Sigh. Might get to 230K today.

Robert

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