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is prime (with the additional constraint that no smaller number satisfying these properties exists). The maximal prime gap G(N) is the length of the largest ...

76 rader · Maximal prime gaps are gaps which are larger than all gaps between smaller primes. Gaps with + before the merit also have larger merit than all gaps between smaller primes. merit = size / log (gap start). The search is exhaustive to 4×10 18 as of 30 December 2015.

If p is a prime, the 'prime gap' after p is the number of composites that follow it. maximal gaps are larger than those for any smaller primes p.

In the following table we list the maximal gaps through 1355. These are the first occurrences of gaps of at least this length . For example, there is a gap of 879 composites after the prime 277900416100927. This is the first occurrence of a gap of this length, but still is not a maximal gap since 905 composites follow the smaller prime

This note presents a result on the maximal prime gap of the form p_(n+1) - p_n <= C(log p_n)^(1+e), where C > 0 is a constant, for any ...

Maximal prime gaps. Definitions for this site: There is a prime gap with positive integers p 1 and p 2 as end points, if p 1 < p 2 are consecutive primes (all intermediate numbers are composites). Some people define p 1 +1 and p 2-1 to be the end points. The size of the prime gap is p 2 - p 1. Some people define it to be one less.

This gap has merit M = 13.1829. The largest known prime gap with identified proven primes as gap ends has length 1113106 and merit 25.90, with 18662-digit ...

Strictly interpreted your result would imply Cramér's conjecture, which as you already said is still open, so a proof is not likely to be forthcoming. But in " Some Conjectures on the Gaps between Consecutive Primes " Wolf gives a heuristic argument to support a similar conjecture that max p n + 1 ≤ N ( p n + 1 − p n) ≈ N π ( N) ( 2 log

We say that gn is a maximal gap, if gm < gn for all m < n . As of August 2018 the largest known maximal prime gap has length 1550, found by Bertil Nyman. It is the 80th maximal gap, and it occurs after the prime 18361375334787046697.

For over a century, mathematicians have understood how the primes taper off on average: Among large numbers, the expected gap between prime ...

updated January 2010) maximal prime gaps, and plot it out against their merit. (Below, in blue.) Let us then take a look at the logarithm of the prime counting function estimate, ln(x/ln(x)), and plot it against the data given above, (in red,) and a correlation arises: Neff’s Merit Conjecture: Merit of Maximal Gaps g n @ A 0 5 10 15 20 25 30 ...

For example, it is conjectured that a gap of size g will appear when the primes are about sqrt(g) * exp(sqrt(g)) in size, or that the maximal prime gap up to n is about (log n)2. On the linked page you'll find more info, a table of known maximal prime gaps, some graphics that show how the various conjectures agree with numerical data.

For any n>1, there is a prime gap of size at least n. The results you read probably meant that it's been proven that the least gap which ...

and maximal prime gaps conclusively established as of the date shown above. In addition, all first known occurrence gaps, less than 2000 in measure, are shown. A supplemental table exhibits all other prime gaps (notfirst occurrences), 1000 or greater in measure, lying below 5e16.

The first occurrence of a gap G is defined by the smallest prime p_k preceding (immediately followed by) such a gap. A (first occurrence of a) gap G is said to ...

A maximal gap is a gap that is strictly greater than all preceding gaps. In other words, a maximal gap is the first occurrence of a gap at least this size.

The maximal prime gaps upper bound problem is one of the major mathematical problems to date. The objective of the current research is to develop a standard which will aid in the understanding of the distribution of prime numbers.

The largest gap between successive prime numbers is unbounded. The larger the prime number, the larger the average gap between it and its successor or ...