oeis A035050,A085427,A063983,A076806
 

I extended [OEIS]035050[/OEIS] "smallest k such that k*2^n + 1 is prime" and [OEIS]085427[/OEIS] "smallest k such that k*2^n - 1 is prime" up to n=10,000:

[URL="http://hoegge.dk/mersenne/b035050.txt"]b035050.txt[/URL]
[URL="http://hoegge.dk/mersenne/b085427.txt"]b085427.txt[/URL]

and [OEIS]063983[/OEIS] "smallest k such that k*2^n +/- 1 are twin primes" up to 5,000:
[URL="http://hoegge.dk/mersenne/b063983.txt"]b063983.txt[/URL]

Hi ATH

How does the twin prime list relate to [url]https://www.mersenneforum.org/showpost.php?p=127890&postcount=38[/url]

Some of the values appear to be the same, but not all of them, especially the early ones. I must've made a mistake somewhere along the line in the generating program.

Beyond 5000 starts at post 111 of the same thread, I did some initial searching and then roger took over, getting up to 16000 at post 243.

We were doing this to find an alternative route to finding large twins. It was a pretty decent collaborative effort on Mersenneforum from about 2008 to 2013. We also looked at a predictive formula for first twins at [url]https://www.mersenneforum.org/showthread.php?t=10063[/url]

I also remember looking at low k prime for the k*2^n+/- and this would have been at the same time, but I'm not sure where this is now on this site.

I did not know about your search, but it is corresponding to [OEIS]076806[/OEIS] "Minimal [B][I]odd[/I][/B] k such that k*2^n-1 and k*2^n+1 are twin primes" while I searched for minimal k (including even k's) [OEIS]063983[/OEIS] "Least k such that k*2^n +/- 1 are twin primes".


The 2 other sequences also have an "odd k's only" version:
[OEIS]057778[/OEIS] "Least odd k such that k*2^n + 1 is prime"
[OEIS]126717[/OEIS] "Least odd k such that k*2^n-1 is prime"

[QUOTE=robert44444uk;513737]Hi ATH

How does the twin prime list relate to [url]https://www.mersenneforum.org/showpost.php?p=127890&postcount=38[/url]

Some of the values appear to be the same, but not all of them, especially the early ones. I must've made a mistake somewhere along the line in the generating program.

Beyond 5000 starts at post 111 of the same thread, I did some initial searching and then roger took over, getting up to 16000 at post 243.

We were doing this to find an alternative route to finding large twins. It was a pretty decent collaborative effort on Mersenneforum from about 2008 to 2013. We also looked at a predictive formula for first twins at [url]https://www.mersenneforum.org/showthread.php?t=10063[/url]

I also remember looking at low k prime for the k*2^n+/- and this would have been at the same time, but I'm not sure where this is now on this site.[/QUOTE]

I collected all the results from the thread from k=1 to k=16,999. I tested them and found 10 errors:
[CODE]470445*2^3670+1 has a small factor : 7 !!
32325705*2^6424+1 is not prime. Proth RES64: 7A48F754F60C4135 Time : 17.073 ms.
15026757*2^6808+1 is not prime. Proth RES64: 05EB3EF08C0895DF Time : 18.904 ms.
55401783*2^7077+1 is not prime. Proth RES64: 91AF6C396CCB095E Time : 20.984 ms.
12004455*2^7989+1 is not prime. Proth RES64: FAA7FCD7C4D69BC7 Time : 22.053 ms.
19939479*2^8366+1 is not prime. Proth RES64: 654147697BBF1557 Time : 27.253 ms.
17000355*2^8367+1 has a small factor : 13 !!
36551361*2^8987+1 is not prime. Proth RES64: 3301DF1440B81D38 Time : 30.436 ms.
6777645*2^10129+1 is not prime. Proth RES64: 0E41D6C782A65B94 Time : 33.628 ms.
84029655*2^16632+1 is not prime. Proth RES64: A6B8753284867C7F Time : 81.115 ms.[/CODE]

I found the correct smallest odd k's for those 10:

[CODE]5109753*2^3670+1 is prime! (1112 decimal digits) Time : 7.078 ms.
57693873*2^6424+1 is prime! (1942 decimal digits) Time : 15.641 ms.
32341743*2^6808+1 is prime! (2057 decimal digits) Time : 17.911 ms.
82676571*2^7077+1 is prime! (2139 decimal digits) Time : 19.356 ms.
34158009*2^7989+1 is prime! (2413 decimal digits) Time : 22.567 ms.
53405475*2^8366+1 is prime! (2527 decimal digits) Time : 24.876 ms.
19939479*2^8367+1 is prime! (2527 decimal digits) Time : 23.020 ms.
44051151*2^8987+1 is prime! (2714 decimal digits) Time : 29.804 ms.
35180031*2^10129+1 is prime! (3057 decimal digits) Time : 57.868 ms.
181076235*2^16632+1 is prime! (5015 decimal digits) Time : 92.955 ms.

5109753*2^3670-1 is prime! (1112 decimal digits) Time : 17.561 ms.
57693873*2^6424-1 is prime! (1942 decimal digits) Time : 23.883 ms.
32341743*2^6808-1 is prime! (2057 decimal digits) Time : 26.614 ms.
82676571*2^7077-1 is prime! (2139 decimal digits) Time : 28.684 ms.
34158009*2^7989-1 is prime! (2413 decimal digits) Time : 29.528 ms.
53405475*2^8366-1 is prime! (2527 decimal digits) Time : 32.877 ms.
19939479*2^8367-1 is prime! (2527 decimal digits) Time : 30.934 ms.
44051151*2^8987-1 is prime! (2714 decimal digits) Time : 35.129 ms.
35180031*2^10129-1 is prime! (3057 decimal digits) Time : 47.675 ms.
181076235*2^16632-1 is prime! (5015 decimal digits) Time : 91.761 ms.
[/CODE]


I checked again and they are now all twin primes, attached is the file corresponding to the sequences on OEIS: [OEIS]076806[/OEIS]

Attached the 3 files corresponding to the 3 OEIS sequences mentioned in the first post.