Math Is Fun Forum

Stangerzv

Member

Registered: 2012-01-30

Posts: 266

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
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9090909090909090909090909090909090909090
9090909090909090909090909090909090909090
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9090909090909090909090909090909090909090
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9090909090909090909090909090909090909090
9090916761247679844122304328506045308491

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

Nehushtan

Member

Registered: 2013-03-09

Posts: 957

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)

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Stangerzv

Member

Registered: 2012-01-30

Posts: 266

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).