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A prime gap of length n is a run of n-1 consecutive composite numbers ... Young and Potler (1989) determined the first occurrences of prime gaps up to ...

First occurrence prime gaps had previously been known for primes less than 4.444 x 1012 [2]. Several gaps larger than the previously largest gap of 682 (not a first occurrence) found by Weintraub [4] have been found. Computer programs were written in FORTRAN and CAL (Cray Assembly Lan- guage) on a CRAY-2 supercomputer.

The following table lists all the first occurrence prime gaps found. ... The maximal first occurrence prime gaps are marked with an asterisk (*).

PDF | We study the first occurrences of gaps between primes in the arithmetic progression (P): r, r + q, r + 2q, r + 3q, ..., where q and r ...

First occurrence prime gaps had previously been known for primes less than 4.444 x 1012 [2]. Several gaps larger than the previously largest gap of 682 (not a first occurrence) found by Weintraub [4] have been found. Computer programs were written in FORTRAN and CAL (Cray Assembly Lan- guage) on a CRAY-2 supercomputer.

The term first known occurrence prime gaprefers to a gap which satisifies conditions (1) and (2) above, but for which condition (3) has not been verified; there may exist a gap (at this time undiscovered, or at least unknown to me) of the same size at some unknown location between the current upper bound of exhaustive

Graham conjecture We can determine a boundary for the first occurance of certain prime gaps if obeying one or more of the two conditions ...

First occurrence prime gaps had previously been known for primes less than 4.444 x 1012 [2]. Several gaps larger than the previously largest gap of 682 (not a first occurrence) found by Weintraub [4] have been found. Computer programs were written in FORTRAN and CAL (Cray Assembly Lan- guage) on a CRAY-2 supercomputer.

First Occurrence Prime Gaps. By Jeff Young and Aaron Potier. Abstract. An ongoing search for first occurrence prime gaps continues.

An ongoing search for first occurrence prime gaps is being carried out which extends all previous work done on this subject. To date this search has found all such gaps for primes up to 7.263 x 1013. First occurrence prime gaps had previously been known for primes less than 4.444 x 1012 [2]. Several gaps larger than the previously largest gap of 682 (not a first occurrence) found by Weintraub [4] have been found.

First occurrence prime gaps. FORMAT Gaps of 1000000 or greater would overflow the standard format, which is described in the principal explanatory notesand employed in the other lists of prime gapsat this site. Consequently, a special format is employed for such gaps. A fictional example is shown below:

The term first known occurrence prime gap refers to a gap which satisifies conditions (1) and (2) above, but for which condition (3) has not been verified; there may exist a gap (at this time undiscovered, or at least unknown to me) of the same size at some unknown location between the current upper bound of exhaustive computation and the listed gap. For prime gap measures whose first occurrence is not yet known, first known occurrences serve as upper bounds; the current upper limit of ...

The growth trend and distribution of the first-occurrence gap sizes are similar to those of maximal gaps between primes in (P). The histograms ...

First occurrence prime gaps had previously been known for primes less than 4.444 x 1012 [2]. Several gaps larger than the previously largest gap of 682 (not a first occurrence) found by Weintraub [4] have been found. Computer programs were written in FORTRAN and CAL (Cray Assembly Lan- guage) on a CRAY-2 supercomputer.

The first occurrence of certain large prime gaps R. Brent Mathematics 1980 The first occurrence of a string of 2r — 1 consecutive composite numbers be- tween two primes (denoted by / (/) and f'r) + 2r) is tabulated for f (r) in the range 2.6 x lu12 <f (r) « 4.444 x 1012. This… Expand 18 PDF View 1 excerpt, references results

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.

A prime gap is the difference between two successive prime numbers. The n-th prime gap, ... For instance, the first prime gap of size larger than 14 occurs between ...

consecutive primes smaller than x and separated by gaps of the length d for d 6 ... 5] J.Young and A.Potler, \First occurrence Prime Gaps", Math.Comp.