mersenneforum.org > Math Dual Riesel problem
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 2006-11-02, 04:19 #1 jasong     "Jason Goatcher" Mar 2005 66638 Posts Dual Riesel problem I've been told(they might be wrong) that another equivalent to the Riesel conjecture(For k*2^n-1 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^n-k.) 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.
 2006-11-02, 16:34 #2 philmoore     "Phil" Sep 2002 Tracktown, U.S.A. 3·373 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.
2006-11-02, 19:28   #3
ET_
Banned

"Luigi"
Aug 2002
Team Italia

32·5·107 Posts

Quote:
 Originally Posted by philmoore 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.
Sure...

 2006-11-02, 21:55 #4 jasong     "Jason Goatcher" Mar 2005 350710 Posts 2^690-9221 2^72-23669 2^1428-23669 2^153-26773 2^60-31859 2^133-38473 2^493-38473 2^51-40597 2^135-40597 2^361-46663 2^83-67117 2^146-81041 2^360-93839 2^480-93839 2^528-93839 2^1080-93839 2^140-97139 2^1451-107347 2^81-113983 2^273-113983 2^329-113983 2^585-113983 2^1905-113983 2^179-114487 2^219-114487 2^539-114487 2^40-121889 2^1328-121889 2^122-141941 2^314-141941 2^638-146561 2^520-161669 2^1178-162941 2^224-191249 2^182-192971 2^61-215443 2^1221-215443 2^37-226153 2^1909-226153 2^97-234343 2^337-234343 2^1090-245561 2^47-250027 2^42-252191 2^60-273809 2^456-273809 2^121-275293 2^1069-275293 2^1741-275293 2^684-315929 2^884-315929 2^306-319511 2^1170-319511 2^50-324011 2^554-324011 2^49-325123 2^265-325123 2^1524-336839 2^69-342673 2^405-342673 2^1628-353159 2^72-362609 2^128-362609 2^457-364903 2^312-365159 2^912-365159 2^1552-365159 2^1624-365159 2^214-368411 2^96-402539 2^496-402539 2^588-402539 2^37-409753 2^61-409753 2^343-415267 2^431-415267 2^887-415267 2^1231-415267 2^63-450457 2^303-450457 2^511-450457 2^895-450457 2^1732-469949 2^129-470173 2^381-470173 2^633-470173 2^46-474491 2^358-474491 2^718-474491 2^958-474491 2^1758-474491 2^291-485557 2^1911-485557 2^83-485767 2^105-494743 Thanks in advance :)
 2006-11-02, 22:28 #5 paulunderwood     Sep 2002 Database er0rr 71738 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 2006-11-02 at 22:29
 2006-11-02, 22:42 #6 philmoore     "Phil" Sep 2002 Tracktown, U.S.A. 3·373 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 web-page 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 2006-11-02 at 22:43
2006-11-03, 23:34   #7
jasong

"Jason Goatcher"
Mar 2005

3·7·167 Posts

Quote:
 Originally Posted by philmoore This dual Riesel project is something that I think Payam Samidoost was interested in, but I don't think he ever got a web-page 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?
Attempting to find "dual" primes for the last 69 k's is my goal. Probably won't prove anything, but it's fun to try.

2007-03-02, 18:14   #8
MooooMoo
Apprentice Crank

Mar 2006

2×227 Posts

Quote:
 Originally Posted by philmoore This dual Riesel project is something that I think Payam Samidoost was interested in, but I don't think he ever got a web-page 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?
Check out this site: http://sierpinski.insider.com/riesel

It hasn't been updated for years, though.

 2007-03-03, 03:13 #9 jasong     "Jason Goatcher" Mar 2005 3·7·167 Posts Here are my results for the left over ks: Code: 123547 2^7-123547 342847 tested to 100000----------------------------sieved 100K-500K 397027 2^19-397027 444637 tested to 10000------------------------------- 2293 tested to 100000-------------------------- 9221 2^6-9221 23669 2^72-23669(pr)(testing)(prime) 26773 2^9-26773 31859 2^12-31859 38473 2^133-38473(pr)(prime) 40597 2^15-40597 46663 2^361-46663(pr)(testing)(prime) 65531 2^16-65531 67117 2^83-67117(pr)(prime) 74699 2^2372-74699(pr)(prime) 81041 2^26-81041 93839 2^360-93839(pr)(prime) 97139 2^20-97139 107347 2^3-107347 113983 2^81-113983 114487 2^3-114487 121889 2^8-121889 129007 2^7-129007 141941 2^2-141941 143047 2^2267-143047(pr)(prime) 146561 2^638-146561(pr)(prime) 161669 2^520-161669(pr)(prime) 162941 2^2-162941 191249 2^224-191249(pr)(prime) 192971 2^182-192971 196597 tested to 100000------------------------------- 206039 2^8-206039 206231 2^22-206231 215443 2^61-215443(pr)(prime) 226153 2^37-226153(pr)(prime) 234343 2^1-234343 245561 2^1090-245561(pr)(prime) 250027 2^47-250027(pr)(prime) 252191 2^42-252191(pr)(prime) 273809 2^12-273809 275293 2^25-275293 304207 tested to 100000---------------------------------- 315929 2^684-315929(pr)(prime) 319511 2^18-319511 324011 2^14-324011 325123 2^49-325123(pr)(prime) 327671 2^2-327671 336839 2^4-336839 342673 2^69-342673(pr)(prime) 344759 tested to 100000--------------------------------- 353159 2^1628-353159(pr)(prime) 362609 2^8-362609 363343 2^13957-363343(pr)==================================================== 364903 2^457-364903(pr)(prime) 365159 2^16-365159 368411 2^22-368411 371893 2^21-371893 384539 2^32672-384539(pr)================================================ 386801 tested to 100000----------------------------- 398023 2^21-398023 402539 2^28-402539 409753 2^37-409753(pr)(prime) 415267 2^343-415267(pr)(prime) 428639 2^8684-428639(pr)(testing in 2) 450457 2^63-450457(pr)(prime) 469949 2^1732-469949(pr)(prime) 470173 2^21-470173 474491 2^46-474491 477583 2^5-477583 485557 2^291-485557 485767 2^11-485767 494743 2^105-494743 502573 2^13-502573 I don't think it's worthwhile to test any further, unless you simply want to find probable primes. Maybe I'm wrong, but I don't think it's possible to test these numbers except in their "general" form. If I'm wrong, someone please post. Last fiddled with by jasong on 2007-03-03 at 03:15
2020-06-03, 17:00   #10
sweety439

"(316^48539+1)/317"
Nov 2016
99(4^34019)99 minima

289310 Posts

Quote:
 Originally Posted by jasong Here are my results for the left over ks: Code: 123547 2^7-123547 342847 tested to 100000----------------------------sieved 100K-500K 397027 2^19-397027 444637 tested to 10000------------------------------- 2293 tested to 100000-------------------------- 9221 2^6-9221 23669 2^72-23669(pr)(testing)(prime) 26773 2^9-26773 31859 2^12-31859 38473 2^133-38473(pr)(prime) 40597 2^15-40597 46663 2^361-46663(pr)(testing)(prime) 65531 2^16-65531 67117 2^83-67117(pr)(prime) 74699 2^2372-74699(pr)(prime) 81041 2^26-81041 93839 2^360-93839(pr)(prime) 97139 2^20-97139 107347 2^3-107347 113983 2^81-113983 114487 2^3-114487 121889 2^8-121889 129007 2^7-129007 141941 2^2-141941 143047 2^2267-143047(pr)(prime) 146561 2^638-146561(pr)(prime) 161669 2^520-161669(pr)(prime) 162941 2^2-162941 191249 2^224-191249(pr)(prime) 192971 2^182-192971 196597 tested to 100000------------------------------- 206039 2^8-206039 206231 2^22-206231 215443 2^61-215443(pr)(prime) 226153 2^37-226153(pr)(prime) 234343 2^1-234343 245561 2^1090-245561(pr)(prime) 250027 2^47-250027(pr)(prime) 252191 2^42-252191(pr)(prime) 273809 2^12-273809 275293 2^25-275293 304207 tested to 100000---------------------------------- 315929 2^684-315929(pr)(prime) 319511 2^18-319511 324011 2^14-324011 325123 2^49-325123(pr)(prime) 327671 2^2-327671 336839 2^4-336839 342673 2^69-342673(pr)(prime) 344759 tested to 100000--------------------------------- 353159 2^1628-353159(pr)(prime) 362609 2^8-362609 363343 2^13957-363343(pr)==================================================== 364903 2^457-364903(pr)(prime) 365159 2^16-365159 368411 2^22-368411 371893 2^21-371893 384539 2^32672-384539(pr)================================================ 386801 tested to 100000----------------------------- 398023 2^21-398023 402539 2^28-402539 409753 2^37-409753(pr)(prime) 415267 2^343-415267(pr)(prime) 428639 2^8684-428639(pr)(testing in 2) 450457 2^63-450457(pr)(prime) 469949 2^1732-469949(pr)(prime) 470173 2^21-470173 474491 2^46-474491 477583 2^5-477583 485557 2^291-485557 485767 2^11-485767 494743 2^105-494743 502573 2^13-502573 I don't think it's worthwhile to test any further, unless you simply want to find probable primes. Maybe I'm wrong, but I don't think it's possible to test these numbers except in their "general" form. If I'm wrong, someone please post.
Are there any newer status (or any large (probable) primes) of this problem? e.g. for the dual Sierpinski problem, there are many large (probable) primes:

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

 2020-06-03, 17:04 #11 sweety439     "(316^48539+1)/317" Nov 2016 99(4^34019)99 minima 11×263 Posts Also, should we allow negative primes? If so, then the smallest remain k is 2293, otherwise, it is 1871.

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