(10^6253*4+11)/3 is 3-PRP! (17.7413s+0.0009s)

[QUOTE=lorgix;234621](10^6253*4+11)/3 is 3-PRP! (17.7413s+0.0009s)[/QUOTE]

If it takes 17 seconds to test a 6254-digit number...

That's a rather slow comp you have;

18333*10^6253+1 is 3-PRP! (0.7094s+0.0003s)

[QUOTE=3.14159;234699]If it takes 17 seconds to test a 6254-digit number...

That's a rather slow comp you have;

18333*10^6253+1 is 3-PRP! (0.7094s+0.0003s)[/QUOTE]

yeah my CPU is obsolete 3 years ago i think and mine can do it in under 3 lol

I wonder what the smallest factors of 2^2^2^6+1, or 2^2^64+1, or 2^18446744073709551616 + 1 are.

Oh.. 2634732075339197803231444993 divides 2^18446744073709551616 + 1

How about.. 2^2^2^10+1?

[QUOTE=3.14159;234717]How about.. 2^2^2^10+1?[/QUOTE]

None known.

[QUOTE=3.14159;234717]I wonder what the smallest factors of 2^2^2^6+1, or 2^2^64+1, or 2^18446744073709551616 + 1 are.

Oh.. 2634732075339197803231444993 divides 2^18446744073709551616 + 1[/QUOTE]

Known since 1986.

[QUOTE=3.14159;234699]If it takes 17 seconds to test a 6254-digit number...

That's a rather slow comp you have;

18333*10^6253+1 is 3-PRP! (0.7094s+0.0003s)[/QUOTE]

I don't remember, but I'm assuming I was running at least Prime95 at the same time.

I say that you lie. Now, back to looking for a prime.. k * 12^13450 + 1 sounds suitable.

Let's say I wanted to find the last 10 or 15 digits of 41 ↑↑ 6, or 41^(41^(41^(41^(41^41)))). I only know that this definitely ends in 41.

Is it similar to 3, which has a certain ending, 9387, whenever one finds the last digits of 3^3^3^3^3^3^3^3^3^... ?

Okay; Now I extended that to 641. 41 ↑↑ 6 ends in 641.

[QUOTE=3.14159;234843]I say that you lie. Now, back to looking for a prime.. k * 12^13450 + 1 sounds suitable.

Let's say I wanted to find the last 10 or 15 digits of 41 ↑↑ 6, or 41^(41^(41^(41^(41^41)))). I only know that this definitely ends in 41.

Is it similar to 3, which has a certain ending, 9387, whenever one finds the last digits of 3^3^3^3^3^3^3^3^3^... ?

Okay; Now I extended that to 641. 41 ↑↑ 6 ends in 641.[/QUOTE]

Are you claiming to know what I remember, or are you claiming to know what I assume? :smile:

115065 * 12[sup]13450[/sup] + 1 (14521 digits)

Verification:

Primality testing 115065*12^13450+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Special modular reduction using zero-padded FFT length 6K on 115065*12^13450+1
Calling Brillhart-Lehmer-Selfridge with factored part 55.77%
115065*12^13450+1 is prime! (5.2899s+0.0017s)

An interesting form of prime;

2 ^ 5 * 3 ^ 662 * 5 ^ 332 * 7 ^ 331 * 11 ^ 332 + 1 (1175 digits)

11581*54^16970+1 (29403 digits)

Verification:

Primality testing 11581*54^16970+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Special modular reduction using zero-padded FFT length 12K on 11581*54^16970+1
Running N-1 test using base 7
Special modular reduction using zero-padded FFT length 12K on 11581*54^16970+1
Calling Brillhart-Lehmer-Selfridge with factored part 82.61%
11581*54^16970+1 is prime! (45.9335s+0.0930s)