20050418, 15:45  #67 
"Sander"
Oct 2002
52.345322,5.52471
29·41 Posts 
I tested n=141 with the old executable upto k=5,555*10^13
This is the closest i got: Code:
43354856050725*2^141+1 is 3PRP! (0.0004s+0.0004s) 43354856050725*2^1411 is 3PRP! (0.0002s+0.0038s) 43354856050725*2^(141+1)+1 is 3PRP! (0.0002s+0.0022s) 43354856050725*2^(141+1)1 is 3PRP! (0.0002s+0.0021s) 2^141+43354856050725 is 3PRP! (0.0001s+0.0021s) 2^14143354856050725 is 3PRP! (0.0001s+0.0030s) 2^(141+1)+43354856050725 is 3PRP! (0.0001s+0.0023s) 2^(141+1)43354856050725 is composite: [2FAAB440A92EB3DC] (0.0001s+0.0022s) 
20050418, 15:52  #68  
Jun 2003
5436_{10} Posts 
Quote:


20050418, 16:41  #69  
Jun 2004
2×53 Posts 
Quote:
I will test k=235 further on! 

20050418, 19:32  #70  
"Sander"
Oct 2002
52.345322,5.52471
1189_{10} Posts 
Quote:
Okay, i'll test 142 then. I'm running the 'sieve' for a day or so on a p3 700 and see what pops up. For 135 i didn't find any upto 1.196*10^13 12 had primes for the first 6 forms, of which 2 had also primes for the 7th form 

20050418, 23:31  #71 
Aug 2004
Melbourne, Australia
2^{3}·19 Posts 
Wow 37!!
So far every test I have put the new program through was passed. So I believe it is working fine.
I ran the complete test on bases upto n=37. (and still going). And that base produced a whopping 83 octoproth primes. Secondly, both bases 32 and 33 have no octoproth primes. Last fiddled with by Dougy on 20050418 at 23:32 
20050419, 02:21  #72 
Aug 2004
Melbourne, Australia
2^{3}×19 Posts 
Hmmm a bug in Dario Alpern's ECM
When I put these (and others) into the batch factorisation:
2^39540206575755 2^39539552526135 and test for primality it says (even if i just type in the decimal too!) 9549238133 is composite 10203287753 is composite However if I factorize them instead 9549238133 = 9549238133 10203287753 = 10203287753 implying they're prime. This means that I will have missed some octoproths... But fortunately I kept the sieved files. URL: http://www.alpertron.com.ar/ECM.HTM 
20050419, 03:56  #73  
Jun 2003
2^{2}·3^{2}·151 Posts 
Quote:
The "deep" version sieves upto p < 10^7, which means that for n <= 45 all the candidates will be automatically prime for 2^n+/k forms! You definitely need to recheck base 32 and 33! Last fiddled with by axn on 20050419 at 03:57 

20050419, 06:16  #74 
Aug 2004
Melbourne, Australia
230_{8} Posts 
Interesting things...
After rechecking the small bases, I've updated the text file again. It should be fixed. I've completed upto n=41. Some interesting properties...
Number of octoprothprimes for n=27,28,29,... 1,2,1,1,2,0,0,7,17,11,90,28,83,331,109,... n=40 alone has 331 octoprothprimes To think only the other day I was hoping to break the 100 mark. Number of kvalues unsieved (octo_deep) for n=27,28,29,... over all possible kvalues. 2,4,4,2,19,22,13,110,137,85,802,360,844,4434,1651,7552,... 
20050419, 08:12  #75  
Jun 2003
1010100111100_{2} Posts 
Quote:
Code:
n = 32  409668105 664495755 2368386195 2709707805 3383804865 3692088225 3762658725 n = 33  715414875 6876947175 n = 34  293705775 1183281975 1397861655 3767954715 4597935705 8596001505 n=35  17182250085 17783238795 20646922695 21811399155 22622064465 23416146075 24115395465 24449183535 25380028905 n=37  7218568995 126139443165 Also, I have checked all high k's for n =27 thru 64 (high k's are k's that can't be reliably sieved because 2^nk becomes smaller than the largest sieve prime). There are no hidden octo's in there 

20050419, 10:09  #76 
Aug 2004
Melbourne, Australia
10011000_{2} Posts 
Wow lots of holes.
Wow thanks, I didn't think there could be so many missing... it's all updated now.
So there might be octo's for all bases after 27. I've added the smallest octo for each base upto 71. Most Wanted: n=72... searched k<1000000000000. 
20050419, 20:09  #77 
"Sander"
Oct 2002
52.345322,5.52471
29·41 Posts 
142
I've found the following for n=142, searching K from 1 to 3.09x10^13
Code:
8444737373415*2^142+1 is 3PRP! (0.0002s+0.0002s) 8444737373415*2^1421 is 3PRP! (0.0002s+0.0023s) 8444737373415*2^(142+1)+1 is 3PRP! (0.0002s+0.0023s) 8444737373415*2^(142+1)1 is 3PRP! (0.0018s+0.0023s) 2^142+8444737373415 is 3PRP! (0.0001s+0.0024s) 2^1428444737373415 is 3PRP! (0.0001s+0.0023s) 2^(142+1)+8444737373415 is 3PRP! (0.0001s+0.0023s) 2^(142+1)8444737373415 is 3PRP! (0.0001s+0.0024s) 9532236817845*2^142+1 is 3PRP! (0.0002s+0.0029s) 9532236817845*2^1421 is 3PRP! (0.0002s+0.0024s) 9532236817845*2^(142+1)+1 is 3PRP! (0.0002s+0.0024s) 9532236817845*2^(142+1)1 is 3PRP! (0.0002s+0.0025s) 2^142+9532236817845 is 3PRP! (0.0001s+0.0023s) 2^1429532236817845 is 3PRP! (0.0001s+0.0023s) 2^(142+1)+9532236817845 is 3PRP! (0.0001s+0.0023s) 2^(142+1)9532236817845 is 3PRP! (0.0001s+0.0026s) 22732824274545*2^142+1 is 3PRP! (0.0002s+0.0003s) 22732824274545*2^1421 is 3PRP! (0.0002s+0.0024s) 22732824274545*2^(142+1)+1 is 3PRP! (0.0002s+0.0024s) 22732824274545*2^(142+1)1 is 3PRP! (0.0002s+0.0024s) 2^142+22732824274545 is 3PRP! (0.0001s+0.0023s) 2^14222732824274545 is 3PRP! (0.0001s+0.0023s) 2^(142+1)+22732824274545 is 3PRP! (0.0001s+0.0024s) 2^(142+1)22732824274545 is 3PRP! (0.0001s+0.0024s) Close to 2 million numbers survived the sieve. Newpgen didn't make sence after this, since it removed candidates much slower than i was able to prp them. I'll try 157 (another 7 mod 15) next. 
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