Utomo Theorem ~ The Next Millenium Prize Problem

Utomo Theorem For every prime numbers p which p + 2 is also prime, then $2^{p+2}$ - 1 always prime.

Can you proves this conjecture?

#NumberTheory

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

but, in f(p) = 2^p - 1 hasn't always gives a prime marsenne.

Budi Utomo - 4 years, 2 months ago

you sure that 2^43 - 1 isn't prime number :(

Budi Utomo - 4 years, 2 months ago

It's actually easier to list the primes $p$ which satisfy your statement than to find the list that fails it. Just compare any list of twin primes with a list of Mersenne primes, and you'll see that the $p$ which satisfy your statement are $p = 3, 5, 11, 17, 29, 59, 1277, 4421, 110501, 132047, \ldots$ and at this point, I got a little tired of looking.

Point being, in the first 8000 or so twin primes, only these 10 satisfy your statement, so there's no way to patch it by removing just a few errant counterexamples.

Brian Moehring - 4 years, 2 months ago

What you mean is the larger one of every twin prime would produce a Mersenne Prime ? Oh I need to check this out

Aditya Narayan Sharma - 4 years, 1 month ago

From this theorem, we knew that a large primes is infinite.

Budi Utomo - 4 years, 2 months ago

Actually, the numbers of the form 2^n-1 that are prime are known as Mersenne primes. Read this

A Former Brilliant Member - 4 years, 2 months ago

For a counter example, take p=41, 2^43-1 is not prime. See this

A Former Brilliant Member - 4 years, 2 months ago

maybe, except just for p = 41.

Budi Utomo - 4 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$