20070415, 05:53  #1 
Jun 2003
5·317 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 
20070415, 08:53  #2 
Jun 2005
101110101_{2} Posts 
I made file for P1 out of it. Whoever takes it, just post your results here as an attachment, no need to send them in.
Yours H. 
20070415, 10:43  #3 
Banned
"Luigi"
Aug 2002
Team Italia
4832_{10} Posts 

20070417, 02:04  #4 
Jun 2003
5·317 Posts 
ET_ any factors yet?

20070417, 11:19  #5 
Banned
"Luigi"
Aug 2002
Team Italia
11340_{8} Posts 

20070418, 02:50  #6 
Jun 2003
1585_{10} 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. 
20070418, 11:21  #7 
Banned
"Luigi"
Aug 2002
Team Italia
12E0_{16} Posts 

20070419, 09:03  #8 
Banned
"Luigi"
Aug 2002
Team Italia
1001011100000_{2} Posts 
Here it is.
Hope the range will finish before I leave Rome for holidays. Luigi 
20070419, 10:29  #9 
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 20070419 at 10:30 
20070419, 14:48  #10 
Banned
"Luigi"
Aug 2002
Team Italia
1001011100000_{2} Posts 

20070419, 19:32  #11 
Jun 2003
5×317 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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