**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?

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

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

Log in to reply

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

Log in to reply

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.

Log in to reply

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

Log in to reply

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

Log in to reply

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

Log in to reply

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

Log in to reply

maybe, except just for p = 41.

Log in to reply