View Single Post
Old 2007-04-15, 05:53   #1
Citrix
 
Citrix's Avatar
 
Jun 2003

32·52·7 Posts
Default 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



Citrix is offline