Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2013-12-10 18:33:02

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Prime Number with (mod11) I Hope it could be new one.

I have encountered a new property in which I hope nobody has found it yet.

The equation is given as follows:

If p is prime and greater than 3 then,

In other words,

If p is prime then

is a whole number.

Prime generated y is given as follows:

y(59)=9090909090909090909090909090909090909090955556068481876491
y(3109)=9090909090909090909090909090 9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
9090916761247679844122304328506045308491

Last edited by Stangerzv (2013-12-10 18:43:41)

Offline

#2 2013-12-10 22:34:01

Nehushtan
Member
From: London
Registered: 2013-03-09
Posts: 602
Website

Re: Prime Number with (mod11) I Hope it could be new one.

The result is not true for p=11. However, if p is odd and not divisible by 11, then it will be true. Here is the proof.

Since p is odd, we have

since 10 ≡ −1 (mod 11). Also

by Fermat’s little theorem. (This only works if p is not divisible by 11.) Hence

Last edited by Nehushtan (2013-12-10 23:47:58)


143 books currently added on Goodreads

Offline

#3 2013-12-10 23:51:21

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: Prime Number with (mod11) I Hope it could be new one.

Thanks Nehustan, I didn't notice when p=11, the same applies to p=3 for mod(3).

Offline

Board footer

Powered by FluxBB