20061102, 04:19  #1 
"Jason Goatcher"
Mar 2005
5·701 Posts 
Dual Riesel problem
I've been told(they might be wrong) that another equivalent to the Riesel conjecture(For k*2^n1 k=509203 is the smallest k for which n always yields a composite) is the dual Riesel conjecture(same thing, but the formula is 2^nk.)
I was wondering if there was a legal(I can't use Primo legally) way to check a k/n pair of that form for primality without taking an overly long amount of time. Thanks in advance. 
20061102, 16:34  #2 
"Phil"
Sep 2002
Tracktown, U.S.A.
5·223 Posts 
Do probable prime tests first, which will eliminate the vast majority of composites. Perhaps if you have some interesting probable primes, someone on the forum who can legally run Primo might check some candidates for you.

20061102, 19:28  #3 
Banned
"Luigi"
Aug 2002
Team Italia
2^{5}×149 Posts 

20061102, 21:55  #4 
"Jason Goatcher"
Mar 2005
5×701 Posts 
2^6909221
2^7223669 2^142823669 2^15326773 2^6031859 2^13338473 2^49338473 2^5140597 2^13540597 2^36146663 2^8367117 2^14681041 2^36093839 2^48093839 2^52893839 2^108093839 2^14097139 2^1451107347 2^81113983 2^273113983 2^329113983 2^585113983 2^1905113983 2^179114487 2^219114487 2^539114487 2^40121889 2^1328121889 2^122141941 2^314141941 2^638146561 2^520161669 2^1178162941 2^224191249 2^182192971 2^61215443 2^1221215443 2^37226153 2^1909226153 2^97234343 2^337234343 2^1090245561 2^47250027 2^42252191 2^60273809 2^456273809 2^121275293 2^1069275293 2^1741275293 2^684315929 2^884315929 2^306319511 2^1170319511 2^50324011 2^554324011 2^49325123 2^265325123 2^1524336839 2^69342673 2^405342673 2^1628353159 2^72362609 2^128362609 2^457364903 2^312365159 2^912365159 2^1552365159 2^1624365159 2^214368411 2^96402539 2^496402539 2^588402539 2^37409753 2^61409753 2^343415267 2^431415267 2^887415267 2^1231415267 2^63450457 2^303450457 2^511450457 2^895450457 2^1732469949 2^129470173 2^381470173 2^633470173 2^46474491 2^358474491 2^718474491 2^958474491 2^1758474491 2^291485557 2^1911485557 2^83485767 2^105494743 Thanks in advance :) 
20061102, 22:28  #5 
Sep 2002
Database er0rr
2^{2}×859 Posts 
Jason, all these numbers can be shown to be prime (or not) using Pari/GP function isprime(). I've just tried the largest and it took about 2 seconds on a Pentium 4 2.4Ghz using half its CPU resources...
Last fiddled with by paulunderwood on 20061102 at 22:29 
20061102, 22:42  #6 
"Phil"
Sep 2002
Tracktown, U.S.A.
5·223 Posts 
Has some program such as pfgw said that these are all probable primes? Actually, I would think that pfgw would be able to show that most are actually prime, not just probable prime. Another possibility is Tony Forbes' VFYPR, which uses the APRCL algorithm, although I have not used it:
http://www.ltkz.demon.co.uk/ar2/vfypr.htm He says that numbers up to around 3300 digits may be tested with it. This dual Riesel project is something that I think Payam Samidoost was interested in, but I don't think he ever got a webpage for it off the ground. Of course, only one prime is needed for each k to eliminate it. Of the 69 remaining k's how many have no known dual prime? Last fiddled with by philmoore on 20061102 at 22:43 
20061103, 23:34  #7  
"Jason Goatcher"
Mar 2005
5×701 Posts 
Quote:


20070302, 18:14  #8  
Apprentice Crank
Mar 2006
11·41 Posts 
Quote:
It hasn't been updated for years, though. 

20070303, 03:13  #9 
"Jason Goatcher"
Mar 2005
5×701 Posts 
Here are my results for the left over ks:
Code:
123547 2^7123547 342847 tested to 100000sieved 100K500K 397027 2^19397027 444637 tested to 10000 2293 tested to 100000 9221 2^69221 23669 2^7223669(pr)(testing)(prime) 26773 2^926773 31859 2^1231859 38473 2^13338473(pr)(prime) 40597 2^1540597 46663 2^36146663(pr)(testing)(prime) 65531 2^1665531 67117 2^8367117(pr)(prime) 74699 2^237274699(pr)(prime) 81041 2^2681041 93839 2^36093839(pr)(prime) 97139 2^2097139 107347 2^3107347 113983 2^81113983 114487 2^3114487 121889 2^8121889 129007 2^7129007 141941 2^2141941 143047 2^2267143047(pr)(prime) 146561 2^638146561(pr)(prime) 161669 2^520161669(pr)(prime) 162941 2^2162941 191249 2^224191249(pr)(prime) 192971 2^182192971 196597 tested to 100000 206039 2^8206039 206231 2^22206231 215443 2^61215443(pr)(prime) 226153 2^37226153(pr)(prime) 234343 2^1234343 245561 2^1090245561(pr)(prime) 250027 2^47250027(pr)(prime) 252191 2^42252191(pr)(prime) 273809 2^12273809 275293 2^25275293 304207 tested to 100000 315929 2^684315929(pr)(prime) 319511 2^18319511 324011 2^14324011 325123 2^49325123(pr)(prime) 327671 2^2327671 336839 2^4336839 342673 2^69342673(pr)(prime) 344759 tested to 100000 353159 2^1628353159(pr)(prime) 362609 2^8362609 363343 2^13957363343(pr)==================================================== 364903 2^457364903(pr)(prime) 365159 2^16365159 368411 2^22368411 371893 2^21371893 384539 2^32672384539(pr)================================================ 386801 tested to 100000 398023 2^21398023 402539 2^28402539 409753 2^37409753(pr)(prime) 415267 2^343415267(pr)(prime) 428639 2^8684428639(pr)(testing in 2) 450457 2^63450457(pr)(prime) 469949 2^1732469949(pr)(prime) 470173 2^21470173 474491 2^46474491 477583 2^5477583 485557 2^291485557 485767 2^11485767 494743 2^105494743 502573 2^13502573 Last fiddled with by jasong on 20070303 at 03:15 
20200603, 17:00  #10  
Nov 2016
924_{16} Posts 
Quote:
Code:
2^16389+67607 2^21954+77899 2^22464+63691 2^24910+62029 2^25563+22193 2^26795+57083 2^26827+77783 2^28978+34429 2^29727+20273 2^31544+19081 2^33548+ 4471 2^38090+47269 2^56366+39079 2^61792+21661 2^73360+10711 2^73845+14717 2^103766+17659 2^104095+7013 2^105789+48527 2^139964+35461 2^148227+60443 2^176177+60947 2^304015+64133 2^308809+37967 2^551542+19249 2^983620+60451 2^1191375+8543 2^1518191+75353 2^2249255+28433 2^4583176+2131 2^5146295+41693 2^9092392+40291 

20200603, 17:04  #11 
Nov 2016
2^{2}·3^{2}·5·13 Posts 
Also, should we allow negative primes? If so, then the smallest remain k is 2293, otherwise, it is 1871.

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