20100221, 07:16  #12 
Nov 2008
2×3^{3}×43 Posts 
Congratulations!
I think we need to coin a new term: vrobable prime 
20100221, 20:24  #13  
Feb 2004
France
922_{10} Posts 
Thanks !
Quote:
Quote:
However, I guess that the probability for a Wagstaff composite to have the VR property is VERY VERY small, if non null. Since VR is based on a Cycle that is of length q (Wq=(2^q+1)/3), I think there is no way that a composite can have VR true. But, without a proof... it is only guesses. Any idea for building a proof of VR ? Read the papers I've gathered on my Blog. It explains many things. If there is something you do not understand, just ask me. Regards, Tony 

20100221, 20:39  #14 
Bemusing Prompter
"Danny"
Dec 2002
California
2^{3}·3·101 Posts 
This is very impressive. I hope it gets proven soon!

20100223, 08:22  #15 
Einyen
Dec 2003
Denmark
3202_{10} Posts 
Congratulations on the new PRP!
Prime95 PRPtest concur :) UID: athath/laptop, 2^4031399+1/3 is a probable prime! Wd4: 2044F973,00000000 
20100223, 08:58  #16 
Jan 2007
Germany
421 Posts 
Congratulation for this nice number !!!!
10 years ago, I tried the Lucas Lehmer Test for this type of numbers. Is it a prime, so the result S=14 or S=194 ( S=2 is for Mp's ), but it is maybe not a proof. 
20100223, 13:58  #17  
Feb 2004
France
2×461 Posts 
Thanks !
Quote:
Which seed did you use ? since you only talk of the last step. Tony 

20100223, 13:59  #18 
Feb 2004
France
2×461 Posts 

20100223, 14:22  #19  
Jan 2007
Germany
421_{10} Posts 
Quote:
You start with S=14, after the LL procedure (S=S^2 mod n)2 you get S=14 or S=194 (14^22). Here the UBASIC program: 10 P=3 20 N=2^P+1 30 T=1:S=14 40 S=(S^2 mod N)2 50 inc T 60 if T=P then print P;S:P=nxtprm(P):goto 20 65 if P>100 then stop 70 goto 40 Here the plot: 3 5 > 5=149 5 14 7 65 > 65=194129 11 14 13 194 17 14 19 194 23 14 29 76653758 31 194 37 42511304261 41 359734364441 43 194 47 17518790332040 53 6406117628425502 59 508334340273339569 61 194 67 21819313749230765027 71 1195598766420873147536 73 5630004848125169115977 79 194 83 5637954672539490707970155 89 20493566371156403602606220 97 68242359663609183220101332858 101 14 103 435037204291375683415946537180 107 32093918361200282030236449354443 109 414278313959563741717336012443446 113 5112917025335077160694569180088809 127 194 131 1973968232982423701206473030341408459198 137 47484206655905551903295319361957840172753 139 168667007687552910631152078108586066160726 149 18453965156596083542114781548941146664272227 151 262976984875073064821485878363989765425623023 157 49547112554957562135729742000244759963364760238 163 898773787877688180281701171238174776273408405979 167 14 173 6874700042006001666774484698531768324621714679913621 179 297595739783471837689716178237652964409196604508541930 181 1244797157598192014982163301734406121591070982512878662 191 14 193 246557495726160777169800308963987254019574345500178382517 197 154344194312622000819873725710721046832719797408900851567781 199 194 next p's are 313 194 347 14 701 14 The same like #7 List of Wagstaff Primes: (2) 3 5 7 11 13 17 19 23 31 43 61 79 101 127 167 191 199 313 347 701 best Last fiddled with by Cybertronic on 20100223 at 14:31 

20100223, 19:26  #20 
Jan 2007
Germany
110100101_{2} Posts 
short addition :
I get with my program: OK list 10 P=3 20 N=2^P+1 30 T=1:S=14 40 S=(S^2 mod N)2 50 inc T 60 if T=P then goto 100 70 goto 40 100 if or{S=(14 mod N),S=(194 mod N)} then print P; 120 P=nxtprm(P):goto 20 OK run 3 5 7 11 13 17 19 23 31 43 61 79 101 127 167 191 199 313 347 701 1709 2617 3539 5807 exact all wagstaff prime exponents in logical order... Last fiddled with by Cybertronic on 20100223 at 19:30 
20100224, 15:46  #21 
Jun 2003
Ottawa, Canada
3×17×23 Posts 
For fun I ran this exponent through my own GMP based VrbaReix PRP code on an Opteron and Core2 to verify and it comes out as prime:
W4031399 is prime! W4031399 = ...2388889642104198122875563 (1213572 digits) Finished! Checked prime q values to: 4031399 Great work DUR! Jeff. 
20100224, 21:35  #22 
Feb 2004
France
2·461 Posts 

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