$\displaystyle 3,5,7$ are primes.

And:

$\displaystyle 7-5=2=5-3$

Question:

Are there any triples of primes so the difference between any two of sequential number equals 2? (Except the above...)

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- Aug 6th 2010, 01:19 PMAlso sprach Zarathustra7-5=2=5-3
$\displaystyle 3,5,7$ are primes.

And:

$\displaystyle 7-5=2=5-3$

Question:

Are there any triples of primes so the difference between any two of sequential number equals 2? (Except the above...) - Aug 6th 2010, 01:56 PMyeKciM
- Aug 6th 2010, 03:04 PMSoroban
Hello, Also sprach Zarathustra!

Quote:

$\displaystyle 3,5,7$ are primes.

And: .$\displaystyle 7-5\:=\:2\:=\:5-3$

Are there any other triples of primes that differ by 2?

Since $\displaystyle 2$ is the only even prime,

. . any such triple of primes must be consecutivenumbers.*odd*

It can be shown that, in a set of three consecutive odd numbers,

. . one of them will be divisible by 3.

Crank out a list of three consecutive odd numbers:

. . $\displaystyle \begin{array}{c}\rlap{/}1-3-5 \\ 3-5-7 \\ 5-7-\rlap{/}9 \\ 7-\rlap{/}9-11 \\ \rlap{/}9-11-13 \\ 11-13-\rlap{//}15 \\ 13-\rlap{//}15-17 \\ \vdots \end{array}$

And we see that $\displaystyle 3-5-7$ is thesuch triple of primes.*only*

- Aug 6th 2010, 03:05 PMundefined
- Aug 6th 2010, 03:17 PMAlso sprach Zarathustra
1 point to Soroban and 1 point to undefined.

- Aug 7th 2010, 06:30 AMwonderboy1953Twin primes
Just to add my two cents worth in, there may be an infinity of twin primes however (Calvin Clawson's [I]Math Mysteries[I] is worthwhile reading).

- Aug 7th 2010, 09:17 AMWilmer
251-257-263-269

4 consecutive primes, any 2 consecutive have same difference (6). - Aug 7th 2010, 10:55 AMundefined
Along those lines,

Green-Tao Theorem - Aug 7th 2010, 12:36 PMWilmer
- Aug 7th 2010, 07:14 PMundefined
:D More nutjob info here

Primes in arithmetic progression - Wikipedia, the free encyclopedia