What Is the Last Prime Quadruplet in the Sequence i, i+2, i+6, i+8?

[ƒ(x) → ∞]

Homework Statement

I am trying to find prime numbers that are i,i+2,i+6,i+8 apart. Could someone tell me the last set that this gives?

Homework Equations

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The Attempt at a Solution

program sieve_t
implicit none
integer*1 s(1000000), offset (10), sequence
integer i, j, n

n=0
sequence=4

do i=1, 10
offset(i)=0
enddo

offset(1)=2
offset(2)=4
offset(3)=2

do i=1, 1000000
s(i) = 1
enddo

do i=2, 1000000
if (s(i).eq.1) then
do j=2, (1000000/i)
s(i*j)=0
enddo
endif
enddo

do i=2, 1000000

if (s(i).eq.1) then
do j=1,sequence-1
if (s(i+offset(j)).ne.1) goto 10
enddo
n=n+1
write(*,*) n, i,i+2,i+6,i+8
endif
10 continue
enddo


end

 

[Mark44]

I'm not sure what you are asking. What does primes that are "i apart" mean? Are you asking for primes that differ by 0, 2, 6, and 8? Primes that differ by 0 aren't very interesting, since they would necessarily be equal. There are lots of primes that differ by 2, the first few pairs of which are 3 and 5, 5 and 7, and 11 and 13.

Please clarify what you're trying to do.

 

[ƒ(x) → ∞]

Sorry Mark44.

I am looking for groups of primes. I am basically looking for prime quadruplets that differ by 2 and 6 and 8.

For example {5, 7, 11, 13}

 

[Mark44]

OK, now I understand. One approach would be to first go through your array of 1,000,000 numbers looking for primes, using the sieve approach as you have been doing. After you have that array of 1s and 0s, then iterate through it looking for a 1. When you find a 1, check whether there is a 1 at position i + 2, i + 6, and i + 8. If there are 1s in all those positions, you have found a prime quadruplet.

 

[ƒ(x) → ∞]

Could you compile it?

 

[Mark44]

Not sure I understand your question. I don't have a Fortran compiler. Did you try my suggestion and get compiler errors? Please clarify what you're asking.

 

[ƒ(x) → ∞]

I think that my compiler has a bug in it, because it cannot even compile a correct code.

Are there any online compilers?