gaps between primes

joan12

is there any formula to compute the gaps between primes which could be true to all prime numbers?..thanks..please help!

vrmuth

we don't have a formula to generate prime numbers , research is going on , if we have such a formula that will also give the gap between two successive primes

Mentallic

Knowing this would make you very rich, wouldn't it?

phinds

How?

Mentallic

I thought I read about it somewhere, but here's a link to such a claim that money is involved with finding large primes:

https://www.eff.org/awards/coop

If there exist formulae to calculate the gaps between primes, then surely they'd be able to find a lot more primes than just searching for all the Mersenne primes.

HallsofIvy

There exist some monetary prizes for math papers but none of them would make you rich!

coolul007

One can create arbitrary large consecutive composite integers by the sequence:
(k+1)! + 2, (k+1)! + 3, ...,(k+1)! + k, (k+1)! + k + 1
This sequence gives you k consecutive integers that are not prime

Mentallic

Well that's the first time I've seen anyone downsize the value of hundreds of thousands of dollars (millions if you include the Millenium prizes).

joan12

. .Thank y0u guys f0r your kind replies. . .I just need s0me ideas to put on with my research paper. .Thanks for sharing, it would be a great help.

haruspex

Try oogling Bertrand's postulate, twin prime conjecture, prime number theorem.

SteveL27

Can you prove that there are arbitrarily large gaps between consecutive primes? In other words there's a gap of a million, a gap of a billion, a gap of a zillion ... you can make the gap between consecutive primes as large as you want. It's an elementary proof, no advanced math needed.

coolul007

The gaps are not necessarily between consecutive primes, they are arbitrarily large consecutive composites.

Diffy

Oh boy..the minute I saw this post I thought:
Given two consecutive primes p1 and p2 the gap between then is |p1 - p2|.
:-D

SteveL27

Sorry, of course that's what I meant :-)

ps -- I see you mentioned this earlier.

eddybob123

There should be a pattern. Primes are not multiples of 2, not multiples of 3, not multiples of 4, etc. Just take the numbers that are not multiples of anything

Mandlebra

Its easy to say "there should be". Try finding it!

Number Nine

So...all we have to do is just take all of the prime numbers? Great.

Your statement isn't even true. Most prime numbers are not multiples of three...