Smallest floor of k for cullen prime

[Citrix]

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

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

[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.

[ET_]

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

[Citrix]

ET_ any factors yet?

[ET_]

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

[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.

[ET_]

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

[ET_]

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

[hhh]

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.

[ET_]

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

[Citrix]

82 values left

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