Re: [PrimeNumbers] Prime Gaps (Was "Prime gaps of 364,188")
- Jose Ramón Brox wrote:
> Well, then what I was asking for, the smallest primes with biggest merit,
> is a subset of that list:
> 2 -->1.44
> 1693182318746371 --> 32.28The two last merits are below Nyman's lucky 32.28 which was record
> 55350776431903243 --> 31.07
> 80873624627234849 --> 31.34
for 6 years. I haven't checked the rest.
> Are there any heuristics to predict the size of the next merit and prime?The Prime Pages has heuristic-based conjectures about large prime gaps:
It doesn't mention merit directly but can be translated to merits.
It says that in 1931 Westzynthius proved there are arbitrarily large merits.
> Are there upper bounds that can never be trespassed, for a given size?Bertrand's postulate (proved by Chebyshev) says there is a prime between
n and 2n.
This gives a weak upper bound on merits for primes below a given size.
Jens Kruse Andersen