20100728, 06:51  #1 
May 2010
111110011_{2} Posts 
k=2003663613 and k=65516468355 primes
This is the k which yielded TPS's first twin. I've tested both the 1 and the +1 sides until n=50K, and the 1 list of primes is below.
Code:
2003663613*2^61 2003663613*2^141 2003663613*2^191 2003663613*2^521 2003663613*2^591 2003663613*2^1081 2003663613*2^1391 2003663613*2^1581 2003663613*2^3961 2003663613*2^4271 2003663613*2^4361 2003663613*2^4841 2003663613*2^5401 2003663613*2^6421 2003663613*2^8061 2003663613*2^9721 2003663613*2^10151 2003663613*2^11761 2003663613*2^12751 2003663613*2^16021 2003663613*2^16381 2003663613*2^16461 2003663613*2^24641 2003663613*2^25001 2003663613*2^26351 2003663613*2^39481 2003663613*2^52021 2003663613*2^80881 2003663613*2^86801 2003663613*2^129421 2003663613*2^129701 2003663613*2^165821 2003663613*2^178351 2003663613*2^226861 2003663613*2^234481 2003663613*2^235801 2003663613*2^372861 2003663613*2^402641 2003663613*2^426791 2003663613*2^570031 2003663613*2^612871 2003663613*2^648841 2003663613*2^666641 2003663613*2^771261 2003663613*2^947871 2003663613*2^969791 2003663613*2^1098281 2003663613*2^1523831 2003663613*2^1873231 2003663613*2^1939561 2003663613*2^1950001 Code:
2003663613*2^21+1 2003663613*2^29+1 2003663613*2^45+1 2003663613*2^64+1 2003663613*2^80+1 2003663613*2^94+1 2003663613*2^150+1 2003663613*2^184+1 2003663613*2^293+1 2003663613*2^428+1 2003663613*2^478+1 2003663613*2^580+1 2003663613*2^704+1 2003663613*2^1501+1 2003663613*2^1518+1 2003663613*2^1532+1 2003663613*2^1628+1 2003663613*2^1925+1 2003663613*2^2422+1 2003663613*2^3845+1 2003663613*2^4294+1 2003663613*2^5488+1 2003663613*2^12381+1 2003663613*2^13662+1 2003663613*2^16940+1 2003663613*2^32741+1 2003663613*2^36909+1 2003663613*2^38613+1 2003663613*2^46868+1 2003663613*2^49589+1 2003663613*2^69317+1 2003663613*2^87910+1 2003663613*2^97740+1 2003663613*2^129397+1 2003663613*2^132632+1 2003663613*2^145134+1 2003663613*2^154988+1 2003663613*2^183092+1 2003663613*2^195000+1 050K: Oddball (complete) 50K195K: PuzzlePeter (complete) This is the k that yielded TPS's second twin. The list of primes for the 1 side is below: Code:
65516468355*2^151 65516468355*2^1811 65516468355*2^2131 65516468355*2^3151 65516468355*2^3731 65516468355*2^6751 65516468355*2^12751 65516468355*2^20231 65516468355*2^47701 65516468355*2^77381 65516468355*2^131221 65516468355*2^176411 65516468355*2^243731 65516468355*2^587111 65516468355*2^2060501 65516468355*2^3333331 Here's the +1 side: Code:
65516468355*2^23+1 65516468355*2^59+1 65516468355*2^81+1 65516468355*2^91+1 65516468355*2^94+1 65516468355*2^113+1 65516468355*2^144+1 65516468355*2^155+1 65516468355*2^173+1 65516468355*2^176+1 65516468355*2^188+1 65516468355*2^219+1 65516468355*2^253+1 65516468355*2^275+1 65516468355*2^289+1 65516468355*2^296+1 65516468355*2^365+1 65516468355*2^443+1 65516468355*2^505+1 65516468355*2^523+1 65516468355*2^600+1 65516468355*2^745+1 65516468355*2^759+1 65516468355*2^949+1 65516468355*2^1000+1 65516468355*2^1033+1 65516468355*2^1268+1 65516468355*2^1435+1 65516468355*2^3216+1 65516468355*2^3721+1 65516468355*2^3728+1 65516468355*2^5089+1 65516468355*2^5583+1 65516468355*2^5588+1 65516468355*2^6115+1 65516468355*2^6480+1 65516468355*2^6505+1 65516468355*2^8436+1 65516468355*2^10896+1 65516468355*2^13907+1 65516468355*2^16635+1 65516468355*2^20264+1 65516468355*2^20709+1 65516468355*2^21105+1 65516468355*2^21263+1 65516468355*2^28323+1 65516468355*2^30845+1 65516468355*2^45420+1 65516468355*2^67296+1 65516468355*2^70983+1 65516468355*2^79625+1 65516468355*2^80756+1 65516468355*2^97171+1 65516468355*2^103856+1 65516468355*2^159247+1 65516468355*2^236464+1 65516468355*2^276270+1 65516468355*2^305518+1 65516468355*2^318484+1 65516468355*2^333333+1 Reservations: 0333333: Merfighters (in progress) Last fiddled with by Oddball on 20101017 at 18:19 
20100728, 07:01  #2  
Mar 2006
Germany
5506_{8} Posts 
Quote:
On the 1 side the series is prim for n=6, 14 and 19 and on the +1 side prime for n=21 and 29! So be sure you know what you're doing and please use srsieve NOT NewPGen for small primes! Last fiddled with by Oddball on 20101010 at 17:31 

20100728, 07:10  #3  
May 2010
499 Posts 
Quote:
Quote:
NewPGen was only used for sieving 5000<=n<=50000. 

20100818, 05:03  #4  
Mar 2010
On front of my laptop
7·17 Posts 
Quote:
Anyway, can I try k=65516468355? (Twin record k) Edit: Can you edit the name of this thread? Last fiddled with by Merfighters on 20100818 at 05:24 

20100818, 05:11  #5 
May 2010
499 Posts 

20100818, 18:05  #6 
May 2010
499_{10} Posts 

20100819, 13:18  #7 
Jun 2009
683_{10} Posts 
OK, I'll fill the gaps 50001  195000 for k=2003663613.
One question: when I run WinPFGW with t switch and I get entries in a file called pfgwprime.log, are they primes or just PRPs to be proven later? Thanks, Peter 
20100819, 13:26  #8  
Nov 2008
2×3^{3}×43 Posts 
Quote:
Secondly, only use the t switch for the +1 side. Use the tp switch for the 1 side. Thirdly, it's faster to run PRP tests (i.e. no t or tp) instead of deterministic tests, then prove the PRPs with t or tp as necessary. 

20100819, 17:49  #9  
Jun 2009
683 Posts 
Quote:


20100819, 19:40  #10  
A Sunny Moo
Aug 2007
USA (GMT5)
3×2,083 Posts 
Quote:
In response to your second question, I'm not sure what you mean; if you're asking whether it switches to a "real" primality test automatically, the answer is no. What you do is first run PFGW to do PRP tests, like this: pfgw l input.txt (or however you're inputting your candidatesif you're using fx to factor the candidates one at a time before testing, you'll want to include that as well) Then, when the range is done, results will be output to pfgw.out, and your PRPs will be output to pfgw.log. Now prove them with: pfgw t pfgw.log (for the +1 side) pfgw tp pfgw.log (for the 1 side) The proven primes will be output to pfgwprime.log. Actually, since you're doing a straightup prime search (as opposed to something fancier like a conjecture search), I would recommend using LLR instead of PFGW for testing. Of course, you'll need to sieve the range first instead of having the numbers factored one at a time prior to PRP testing; but it shouldn't take long to sieve to a reasonably optimal depth for numbers this small. The nice thing about using LLR is that it does a "real" primality test right from the getgo, but since it's doing an LLR or Proth test instead of an N1/N+1, there's no speed penalty to using the full primality test. (Note that some of what I've said above is incorrect for bases other than 2, but your search here is strictly base 2 so I didn't bother expounding in that direction.) Last fiddled with by mdettweiler on 20100819 at 19:41 Reason: typo 

20100819, 20:09  #11 
Jun 2009
683 Posts 
That's exactly what I was wondering about, thank you!
This is unknown territory for me. I did and do a lot of manual sieving and LLRing for Prime Grid, but I never had to create the candidate files. First I thought about using NewPGen for sieving, but this is a fixedk search. Using the "increase n by 1" option would have given me 145,000 files with one or zero candidates each, right? That's why I preferred PFGW. After reading the documentation I realized the input file was only two lines and created within a few seconds ;) Right, so I switched to PRPing and will do the conclusive primality tests only for the PRPs. Something related: I tried using LLR on candidates of the form k*b^n1 with b =/= 2 and the output was giving me "not prime" or "PRP". Can I use PFGW for the final primality test on these PRPs? Sorry for stretching your patience... 
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