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 2007-04-15, 05:53 #1 Citrix     Jun 2003 62E16 Posts Smallest floor of k for cullen prime A related problem to the project. Find the smallest floor of k for a cullen prime? eg. 18496*2^18496+1 is prime and 18496=2^4*17^2. Hence 17 is the floor of the k for this prime. what is the smallest floor value, a Cullen prime can have? (1*2^1+1 does not count) Looking at 2^n*2^(2^n)+1 then n+2^n must be equal to 2^m (This is not possible) So what about k=2^x*3^y? I looked at values with floor<=13 and k=1.5M to 5M and sieved to p=2.5G Values left=96 Code: 1522521 2 +1 1542294 2 +1 1544400 2 +1 1548288 2 +1 1607445 2 +1 1660932 2 +1 1670625 2 +1 1702701 2 +1 1711125 2 +1 1774500 2 +1 1791153 2 +1 1835008 2 +1 1837500 2 +1 1848000 2 +1 1848015 2 +1 1976832 2 +1 1980825 2 +1 2027520 2 +1 2037420 2 +1 2047032 2 +1 2050048 2 +1 2076165 2 +1 2079000 2 +1 2096640 2 +1 2112000 2 +1 2167074 2 +1 2200000 2 +1 2207205 2 +1 2222640 2 +1 2258685 2 +1 2293200 2 +1 2321865 2 +1 2359296 2 +1 2371600 2 +1 2376990 2 +1 2396160 2 +1 2415765 2 +1 2416128 2 +1 2419200 2 +1 2469852 2 +1 2480625 2 +1 2578125 2 +1 2704000 2 +1 2772000 2 +1 2788500 2 +1 2810808 2 +1 2881200 2 +1 2889432 2 +1 2918916 2 +1 2940000 2 +1 2956800 2 +1 2976750 2 +1 2988216 2 +1 3000000 2 +1 3007125 2 +1 3080025 2 +1 3130218 2 +1 3243240 2 +1 3279276 2 +1 3281250 2 +1 3294225 2 +1 3294720 2 +1 3312400 2 +1 3369600 2 +1 3388000 2 +1 3430000 2 +1 3435432 2 +1 3440640 2 +1 3503500 2 +1 3592512 2 +1 3639168 2 +1 3649536 2 +1 3651921 2 +1 3704778 2 +1 3748096 2 +1 3773952 2 +1 3802500 2 +1 3893760 2 +1 3931200 2 +1 3936600 2 +1 3960000 2 +1 4009500 2 +1 4026880 2 +1 4077216 2 +1 4164160 2 +1 4198467 2 +1 4276800 2 +1 4392300 2 +1 4563000 2 +1 4658500 2 +1 4764375 2 +1 4791600 2 +1 4840000 2 +1 4851495 2 +1 4915625 2 +1 4919376 2 +1
2007-04-15, 08:53   #2
hhh

Jun 2005

373 Posts

I made file for P-1 out of it. Whoever takes it, just post your results here as an attachment, no need to send them in.

Yours H.
Attached Files
 worktodo.ini (3.2 KB, 319 views)

2007-04-15, 10:43   #3
ET_
Banned

"Luigi"
Aug 2002
Team Italia

482510 Posts

Quote:
 Originally Posted by hhh I made file for P-1 out of it. Whoever takes it, just post your results here as an attachment, no need to send them in. Yours H.
I will take it.

Luigi

 2007-04-17, 02:04 #4 Citrix     Jun 2003 2×7×113 Posts ET_ any factors yet?
2007-04-17, 11:19   #5
ET_
Banned

"Luigi"
Aug 2002
Team Italia

113318 Posts

Quote:
 Originally Posted by Citrix ET_ any factors yet?
Yes, I guess... But I usually wait until the end of the worktodo file before posting them. If you need factors, I'll give you factors.

Luigi

 2007-04-18, 02:50 #6 Citrix     Jun 2003 30568 Posts I want to sieve these numbers. So every number removed would speed up the sieve very much as there are only 96 numbers. Please post the factors or PM them to me. Thanks.
2007-04-18, 11:21   #7
ET_
Banned

"Luigi"
Aug 2002
Team Italia

113318 Posts

Quote:
 Originally Posted by Citrix I want to sieve these numbers. So every number removed would speed up the sieve very much as there are only 96 numbers. Please post the factors or PM them to me. Thanks.
Sure!

I will as I get home.

Luigi

2007-04-19, 09:03   #8
ET_
Banned

"Luigi"
Aug 2002
Team Italia

52×193 Posts

Quote:
 Originally Posted by ET_ Sure! I will as I get home. Luigi
Here it is.

Hope the range will finish before I leave Rome for holidays.

Luigi
Attached Files
 results.txt (9.3 KB, 317 views)

 2007-04-19, 10:29 #9 hhh     Jun 2005 373 Posts The factors extracted, that is: 1544400*2^1544400+1 has a factor: 296422789591 1670625*2^1670625+1 has a factor: 17013078193 1835008*2^1835008+1 has a factor: 1806740003779 1848000*2^1848000+1 has a factor: 205711170389 1976832*2^1976832+1 has a factor: 553932275329 2222640*2^2222640+1 has a factor: 137501949437 2321865*2^2321865+1 has a factor: 891027736803831101 2371600*2^2371600+1 has a factor: 11820909853 2578125*2^2578125+1 has a factor: 1959727987549 2810808*2^2810808+1 has a factor: 23310569324950301 2889432*2^2889432+1 has a factor: 7434991684639 3279276*2^3279276+1 has a factor: 190732308121 4009500*2^4009500+1 has a factor: 104002452629 4077216*2^4077216+1 has a factor: 3372457757 4198467*2^4198467+1 has a factor: 262214394002536659168487 Just post your latest result before leaving, sombody else will finish it, I bet. H. Last fiddled with by hhh on 2007-04-19 at 10:30
2007-04-19, 14:48   #10
ET_
Banned

"Luigi"
Aug 2002
Team Italia

52·193 Posts

Quote:
 Originally Posted by hhh Just post your latest result before leaving, sombody else will finish it, I bet. H.
Now I'm reasonably sure I can finish the entire range, thanks.

Luigi

 2007-04-19, 19:32 #11 Citrix     Jun 2003 2·7·113 Posts 82 values left Code: 1522521 2 +1 1542294 2 +1 1548288 2 +1 1607445 2 +1 1660932 2 +1 1702701 2 +1 1711125 2 +1 1774500 2 +1 1791153 2 +1 1837500 2 +1 1848015 2 +1 1980825 2 +1 2027520 2 +1 2037420 2 +1 2047032 2 +1 2050048 2 +1 2076165 2 +1 2079000 2 +1 2096640 2 +1 2112000 2 +1 2167074 2 +1 2200000 2 +1 2207205 2 +1 2258685 2 +1 2293200 2 +1 2321865 2 +1 2359296 2 +1 2376990 2 +1 2396160 2 +1 2415765 2 +1 2416128 2 +1 2419200 2 +1 2469852 2 +1 2480625 2 +1 2704000 2 +1 2772000 2 +1 2788500 2 +1 2881200 2 +1 2918916 2 +1 2940000 2 +1 2956800 2 +1 2976750 2 +1 2988216 2 +1 3000000 2 +1 3007125 2 +1 3080025 2 +1 3130218 2 +1 3243240 2 +1 3281250 2 +1 3294225 2 +1 3294720 2 +1 3312400 2 +1 3369600 2 +1 3388000 2 +1 3430000 2 +1 3435432 2 +1 3440640 2 +1 3503500 2 +1 3592512 2 +1 3639168 2 +1 3649536 2 +1 3651921 2 +1 3704778 2 +1 3748096 2 +1 3773952 2 +1 3802500 2 +1 3893760 2 +1 3931200 2 +1 3936600 2 +1 3960000 2 +1 4026880 2 +1 4164160 2 +1 4276800 2 +1 4392300 2 +1 4563000 2 +1 4658500 2 +1 4764375 2 +1 4791600 2 +1 4840000 2 +1 4851495 2 +1 4915625 2 +1 4919376 2 +1

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