Challenge

[science_man_88]

all I wanted to do is find a pattern that could back up my previous one about the 4 x th prime then I can give you a range to check and find a new one. also last I checked the source i read said the next one is likely in the 63 million exponent range and will have 19 million digits.


by a pattern to back up the other one I mean a pattern in the 4 xth prime to go to or the amount x increases for the next one to check around.

[Mini-Geek]

Originally Posted by flouran

In the event that he does give us a big number (beyond testing limits with ECPP or LL), we could use a probabilistic primality test. If the number is declared composite, then it is 100% true. If the number is declared prime, then it is most likely prime. In the event that he gives us a pseudoprime, it can be no larger than 2^64, which is well within testing limits.

This is described in further detail here:
http://mersenneforum.org/showpost.ph...94&postcount=5

Of course, we would most likely have to code an M-R test, which is not hard to do; especially since a probabilistic primality test like OPQBT or RQFT (which has a worst case error estimate of much less than 1/4) is yet to be optimized and coded in full.

For one that would need ECPP, sure, we could PRP it first.
Maybe I'm missing something, but if it could be done with the LL wouldn't that be about as fast as a PRP test?

[Dougal]

63 million is a total guess really.noone can say where the next prime will be.you said about 6 hours hours ago that you could find 48000 mersenne primes a year with 9 computers.ok,so you have one computer,thats 48000/9=5333.so on your own in a year you could find this many mersenne primes.5333/365=14.6 so you could find this many in one day.6 hours is a quarter of a day so 14.6/4=3.65 you should have found at least 3 mersenne primes by now,where are they?

[science_man_88]

3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71
73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173
179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281
283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409
419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541
547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659
661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809
811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941
947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069
1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223
1229


RED = 4 xth odd prime
YELLOW = mersenne exponent

[Dougal]

and can you explain what this is telling us?

[science_man_88]

if I could find a pattern in the number of 4 x th odd primes between each know exponent maybe I could say this is the closest 4 xth odd prime to this exponent so go this many 4 xth odd primes and check the 4 primes on each side and or itself .

[Dougal]

what is 4 x th stuff about, are you saying for example take x=3,so 4*3=12,the nearest prime is either 11 or 13 so an exponent near 11 or 13 will yield a prime?

[flouran]

Originally Posted by Mini-Geek

For one that would need ECPP, sure, we could PRP it first.
Maybe I'm missing something, but if it could be done with the LL wouldn't that be about as fast as a PRP test?

Yep. But PRP is better for testing composites (which most likely will be science man's "prime"); hence, their nickname, the "compositeness test". I wouldn't object to LL, though.

Although M-R and LL run in the same asymptotic time, I suggested M-R because it is way way way easier to code in PARI/GP than it is to code LL (apparently, my stupidity was at an all-time-high because I had been incognizant of Ernst's code ).

[science_man_88]

No I'm saying the fourth odd prime is 11 so in this case if you look both side you can find at least one prime exponent that works and because it's more than one 4 x th odd prime before the next in the hundreds I'd need a pattern of how many between the next possibility

[10metreh]

Originally Posted by science_man_88

No I'm saying the fourth odd prime is 11 so in this case if you look both side you can find at least one prime exponent that works and because it's more than one 4 x th odd prime before the next in the hundreds I'd need a pattern of how many between the next possibility

This is not the sort of place you'll find patterns. Somewhere you might is en.wikipedia.org/wiki/Mandelbrot_set.

[science_man_88]

also it might tell us which ones have a digit number divisible by 3 if you look though 31 doesn't work for this case ( no surprise for me there) both of the other ones shown that are halfway between the 4 x th odd primes according to wikipedia have digit numbers divisible by 3.