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-   -   1000039*2^n+1 (https://www.mersenneforum.org/showthread.php?t=26614)

 Alex 2021-03-15 22:02

1000039*2^n+1

Hello.
I`m working on [B]1000039*2^n+1[/B] with n=[1..2.000.000] (k=1.000.039 is wellsieved).
Now it was passed n=[1..1.000.000] (8150 tests).

[CODE]1000039*2^382+1 is prime! (121 decimal digits) Time : 119.587 ms.
1000039*2^466+1 is prime! (147 decimal digits) Time : 45.074 ms.
1000039*2^670+1 is prime! (208 decimal digits) Time : 48.150 ms.
1000039*2^1414+1 is prime! (432 decimal digits) Time : 41.688 ms.
1000039*2^8326+1 is prime! (2513 decimal digits) Time : 239.942 ms.
1000039*2^10810+1 is prime! (3261 decimal digits) Time : 390.164 ms. - [URL="https://primes.utm.edu/primes/page.php?id=29207"]First found in 1997 by Steffen Polster (SP code)[/URL]
1000039*2^13102+1 is prime! (3951 decimal digits) Time : 642.368 ms. - [URL="https://primes.utm.edu/primes/page.php?id=27534"]First found in 1997 by Steffen Polster (SP code)[/URL][/CODE]

It was no new primes :sad:

Does anybody want to join me to finish the rest ~7650 tests?

The range was sieved up to p=21e12 (~40 min per factor).
PFGW / LLR is ~20 min per test.

 rogue 2021-03-15 23:35

[QUOTE=Alex;573807]Hello.
I`m working on [B]1000039*2^n+1[/B] with n=[1..2.000.000] (k=1.000.039 is wellsieved).
Now it was passed n=[1..1.000.000] (8150 tests).

[CODE]1000039*2^382+1 is prime! (121 decimal digits) Time : 119.587 ms.
1000039*2^466+1 is prime! (147 decimal digits) Time : 45.074 ms.
1000039*2^670+1 is prime! (208 decimal digits) Time : 48.150 ms.
1000039*2^1414+1 is prime! (432 decimal digits) Time : 41.688 ms.
1000039*2^8326+1 is prime! (2513 decimal digits) Time : 239.942 ms.
1000039*2^10810+1 is prime! (3261 decimal digits) Time : 390.164 ms. - [URL="https://primes.utm.edu/primes/page.php?id=29207"]First found in 1997 by Steffen Polster (SP code)[/URL]
1000039*2^13102+1 is prime! (3951 decimal digits) Time : 642.368 ms. - [URL="https://primes.utm.edu/primes/page.php?id=27534"]First found in 1997 by Steffen Polster (SP code)[/URL][/CODE]

It was no new primes :sad:

Does anybody want to join me to finish the rest ~7650 tests?

The range was sieved up to p=21e12 (~40 min per factor).
PFGW / LLR is ~20 min per test.[/QUOTE]

If you have a good GPU, then you should be using srsieve2cl for sieving this sequence. If anything you might want to compare its speed to sr1sieve.

 bur 2021-03-23 08:37

The number of candidates for n < 1,000,000 seems so small for p < 21e12. I sieved k=1281979 up to p = 312e12 and was left with nearly 15,000 candidates for n < 1,000,000.

And as rogue said, definitely use sr1sieve. It is by far the fastest for this type of search. For the Proth test, do you use LLR2? It has Gerbicz error correction which is very useful when working alone (i.e. no double checking).

And best of luck to you! I tested all n < 2,500,000 on "my" k so far and the last prime occured around n = 415,000. I hope I'll find at least one more prime until the end of the sieve at n = 4,100,000.

 Happy5214 2021-03-23 09:00

[QUOTE=bur;574412]For the Proth test, do you use LLR2? It has Gerbicz error correction which is very useful when working alone (i.e. no double checking).[/QUOTE]

Doesn't "standard" LLR have Gerbicz error correction for Proth tests as of 3.8.24? I know it defaults to Fermat PRP tests with GBC for Riesel candidates now, so I would assume Jean's implemented it for Proth tests too.

 Alex 2021-03-23 12:54

Thank you, rogue.

Thank you, bur.
I`ve chosen k=1000039 because it is wellsieved.
For the comparison sieving n=[1..1000000] up to p<1e6:
k=1000039 has 16891 candidates
k=1281979 has 39706 candidates

k=1000039 has only 7 known small primes, it is not Sierpinski number.
Now I have found several less candidates k, but k=1000039 was the first.
I use Sr1sieve & PFGW.

 rogue 2021-03-23 15:33

[QUOTE=Alex;574417]Thank you, rogue.

Thank you, bur.
I`ve chosen k=1000039 because it is wellsieved.
For the comparison sieving n=[1..1000000] up to p<1e6:
k=1000039 has 16891 candidates
k=1281979 has 39706 candidates

k=1000039 has only 7 known small primes, it is not Sierpinski number.
Now I have found several less candidates k, but k=1000039 was the first.
I use Sr1sieve & PFGW.[/QUOTE]

llr is probably faster than pfgw for these numbers.

 Alex 2021-08-03 13:59

Hello.
Yesterday I`ve got a new result beautiful enough:

[CODE]1000039*2^1721722+1 is prime! (518296 decimal digits) Time : 1944.927 s. - [URL="https://primes.utm.edu/primes/page.php?id=132580"]Found in 2021 (P420 code)[/URL][/CODE]

Soon I`ll finish the rest of my range.

 bur 2021-08-12 06:25

Great, congratulations! Even large enough for a nice entry in Caldwell's list!

Sadly, my k=1281979 hasn't produced a prime since 485014 and I'm at n ~ 4,600,000 now... :D

 Alex 2021-09-23 14:53

Thank you, bur.

I have finished my range:
[B]1000039*2^n+1[/B] with [B]n=[1..2.000.000][/B]
Totally passed 15.825 tests.
Confirmed 7 old primes and found 1 new :-)

[CODE]1000039*2^382+1 is prime! (121 decimal digits) Time : 119.587 ms.
1000039*2^466+1 is prime! (147 decimal digits) Time : 45.074 ms.
1000039*2^670+1 is prime! (208 decimal digits) Time : 48.150 ms.
1000039*2^1414+1 is prime! (432 decimal digits) Time : 41.688 ms.
1000039*2^8326+1 is prime! (2513 decimal digits) Time : 239.942 ms.
1000039*2^10810+1 is prime! (3261 decimal digits) Time : 390.164 ms. - [URL="https://primes.utm.edu/primes/page.php?id=29207"]First found in 1997 by Steffen Polster (SP code)[/URL]
1000039*2^13102+1 is prime! (3951 decimal digits) Time : 642.368 ms. - [URL="https://primes.utm.edu/primes/page.php?id=27534"]First found in 1997 by Steffen Polster (SP code)[/URL]
[COLOR="Red"]1000039*2^1721722+1 is prime! (518296 decimal digits) Time : 1944.927 s. - [URL="https://primes.utm.edu/primes/page.php?id=132580"]Found in 2021 (P420 code)[/URL][/COLOR][/CODE]

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