PARI's commands

[CRGreathouse]

Originally Posted by science_man_88

what you want to calculate is:

http://www.research.att.com/~njas/sequences/A070325

Good catch. Related: http://oeis.org/classic/A127435

[science_man_88]

for(n=1, 33000, if(isprime(n^2+1)*isprime(n^4+1)*isprime(n+1)==1, print1(n, ", ")))

that's the code that's up on http://www.research.att.com/~njas/sequences/A070325 but why multiply you still have to calculate isprime() to check it, is it faster than && ?

[3.14159]

Originally Posted by CRGreathouse

A number x is in the set of squares and the set of fourth powers.

is the same as

A number x is in the the set of fourth powers.

This one falls apart really quickly.

This would only be true if the set of squares were all fourth powers as well.

25 is a square number and is not a 4th power.
625 is a square number and is a fourth power.

49 is a square number that is not in the set of fourth powers.
2401 is a square number that is in the set of fourth powers.

[CRGreathouse]

Back on topic:

Originally Posted by 3.14159

Wait.. Prime fermat numbers are probably finite for any given base. So there are no examples for 120!. That explains it.

For item 16: There are probably no 1000+ digit examples.

Due to that, this is the only category that will be restricted to small primes, 100-750 digits.

If you find me a 1000+ digit example, the restriction will be lifted.

With n = 3 · 2⁴¹⁰⁸⁵⁷, n + 1, n² + 1, and n⁴ + 1 are primes. Since 494724 ≥ 1000, I trust you'll be lifting the restriction?

[3.14159]

Originally Posted by CRGreathouse

With n = 3 · 2⁴¹⁰⁸⁵⁷, n + 1, n² + 1, and n⁴ + 1 are primes. Since 494724 ≥ 1000, I trust you'll be lifting the restriction?

Restriction lifted.

[science_man_88]

Originally Posted by CRGreathouse

Good catch. Related: http://oeis.org/classic/A127435

I could see if it was faster but according to a few test of each mine is about 40 times faster and I think I know why based on my knowledge of what the comparison in ASM might be like.

mine uses 2 cmp operations

the one shown uses 1 cmp and 3 mult() ? operations (not sure if this makes the difference though) as i don't know how much slower / faster multiplication is comparing it to a cmp() operation.

[CRGreathouse]

Originally Posted by 3.14159

This one falls apart really quickly.

Really? Please provide an example of a member of the set of fourth powers that is not a member of the set of squares and the set of fourth powers, or a member of the set of squares and the set of fourth powers, but not a member of the set of fourth powers.

[CRGreathouse]

Originally Posted by science_man_88

I could see if it was faster

What is "it"?

Originally Posted by science_man_88

mine uses 2 cmp operations

the one shown uses 1 cmp and 3 mult() ? operations (not sure if this makes the difference though) as i don't know how much slower / faster multiplication is comparing it to a cmp() operation.

imul takes about 4 times as long as cmp. fmul is similar. For older CPUs, cmp was relatively better.

[3.14159]

Originally Posted by CRGreathouse

Really? Please provide an example of a member of the set of fourth powers that is not a member of the set of squares and the set of fourth powers, or a member of the set of squares and the set of fourth powers, but not a member of the set of fourth powers.

There is no such example, but there is no redundancy.

Here's another example:

169 is a square number, and it is not a fourth power.
28561 is a square number, and it is also a fourth power.

Or:

169 is in set x but is not in set y.
28561 is in set x and is in set y.

All members of set y are in set x.
Not all members of set x are in set y.

[science_man_88]

Originally Posted by CRGreathouse

What is "it"?



imul takes about 4 times as long as cmp. fmul is similar. For older CPUs, cmp was relatively better.

that's why mine gave me times of 10-20 ms but the other gave me 600-650? ms

thanks I think if we want fast code in the OEIS the code shown should be changed for it= http://www.research.att.com/~njas/sequences/A070325

[CRGreathouse]

Originally Posted by 3.14159

There is no such example, but there is no redundancy.

Here's another example:

169 is a square number, and it is not a fourth power.
28561 is a square number, and it is also a fourth power.

Or:

169 is in set x but is not in set y.
28561 is in set x and is in set y.

No redundancies.

Ah, so you just don't understand the word "redundancy".