PARI's commands

[CRGreathouse]

Originally Posted by science_man_88

I find all the terms except the first have a digital root of 4 or 1 just like the Mersenne primes >7 if we could confirm something like a pattern (I think starting at the 4th term they may take on the opposite to the series for the Mersenne primes>31) if this was ever proven true it could let us look 4 Mersenne primes in the future(that's why I'm doubtful).

Digital roots are essentially the number mod 9. Mersenne numbers other than 3 are of the form 2^(2k+1) - 1 = 4^k * 2 - 1, which is 1 mod 3. Thus Mersenne numbers other than 3 are 1, 4, or 7 mod 9. Further, the numbers are 7 mod 9 only when the exponent is a multiple of 3, which for Mersenne primes happens only with M_3 = 7. So the product of two Mersenne primes, both greater than 7, will be 1*1, 1*4, 4*1, or 4*4 mod 9, that is, will have digital root 1, 4, or 7.

You only gave the first two possibilities, but the third happens with
(2⁸⁹ - 1)(2¹⁰⁷ - 1) = 100433627766186892221372630609062766858404681029709092356097
and presumably occurs infinitely often.

[CRGreathouse]

Originally Posted by 3.14159

The law of small numbers, at work again. Unless you can definitively prove this, it is nothing more than a guess.

It seems to show that science_man_88's intuition is pretty sharp vis-a-vis the strong law of small numbers, actually. Although he did miss one case, I guess because it wasn't listed in A165223.

[3.14159]

Originally Posted by CRGreathouse

It seems to show that science_man_88's intuition is pretty sharp vis-a-visthe strong law of small numbers, actually. Although he did miss one case, I guess because it wasn't listed in A165223.

Remember: Just because it works for three examples, doesn't mean it works forever.

[science_man_88]

Originally Posted by 3.14159

Remember: Just because it works for three examples, doesn't mean it works forever.

funny I checked every one it the sequence.

[3.14159]

Also: Are there any sieving programs for n * k! + 1 ?

Nevermind: PARI does the work here. I'll set up a program which can act as an amateur sieve:

kfacsieve(x, n, a, m) = {
for(p=x,n,
if((x*n+1)%p==0, ...

[science_man_88]

Originally Posted by 3.14159

Also: Are there any sieving programs for n * k! + 1 ?

Nevermind: PARI does the work here. I'll set up a program which can act as an amateur sieve:

kfacsieve(x, n, a, m) = {
for(p=x,n,
if((x*n+1)%p==0, ...

I got

for(n=1,100,for(k=1,100,if(isprime(n*k!+1),print(n","k))))

[3.14159]

Without using (isprime(x))

Also: @CRG: I tried this:

 d(a,n,x,m)=for(n=a,x,if(t(n*m!+1)!=n,print("trivial composite","factor is",t(n*m!+1)));if(t(n*m!+1)==n,print(n*m!+1)))

Where t(n) is trial division up to nextprime(10^6).

I get the error: "Too many parameters in user-defined function".

I don't see where the excess params are at: I introduced no new variables into the commands. Or is it treating t as a variable?

[CRGreathouse]

Originally Posted by 3.14159

Also: Are there any sieving programs for n * k! + 1 ?

What's fixed?

[3.14159]

Originally Posted by CRGreathouse

What's fixed?

k is fixed, n is variable.

Reason: Primeform too slow!

[science_man_88]

Originally Posted by 3.14159

k is fixed, n is variable.

Reason: Primeform too slow!

I got

 not a function: `t'.

posting it into pari.

[3.14159]

Because you have not defined t yet. I have.