# Prime pattern

I am curious as to whether this pattern will always hold true:

Let's say we take the prime numbers:
2,3,5,7,11,13,17,19,23.......primes
and we take the square(individually) minus 1
3,8,24,48,120,168,288,360,528....p^2 - 1

Then starting with the third p^2 - 1 (24), all of the p^2 - 1 can be rewritten as and earlier p^2-1 times a prime # (or multiple prime #'s)

for example: 24=8x3,48=24x2,528=48x11,...and so on.

Is this at all interseting or just something stupid that I am missing?

Let me know,
Thanks

Hurkyl
Staff Emeritus
Gold Member
p^2-1 times a prime # (or multiple prime #'s)
Why not just say "p²-1 times a number"?

It's a rather trivial observation; 3 is on your list.

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The number 4 times out of five is a single prime #. It seemed a lot nicer when i posted it and in the first ten i checked 9 of them were single prime numbers. I have since found 3 more where the # is a multiple of 2 primes (2 and 3 in all cases). Thanks for at least looking at it Hurkyl

Hurkyl
Staff Emeritus