[seqfan] A look at prime number gaps using only potential prime numbers

[Harry Neel]

Looking at a sieve for all numbers having factors greater than 5 and selecting choosing numbers that have factors equal to greater than 7 it appears that a lists of “Maximal Gaps’ that is based on where potential prime locations are not prime numbers.  For example 49 is the first potential prime location that is not prime having a prime factor of 7.

The preceding prime is 47 and the next number which could be prime is 53, which is prime. So is there a maximal gap in the potential prime locations of 1?

Unless mistakes were made, the gaps below are straight from sieving.

Gap of                 following prime
1                                               47
2                                             113
3                                              317
4                                              523
8                                              1327
9                                              9551
10                                           15683

Only preliminary checks on additional gaps have been preformed and Maximal Gap lengths may not be appropriate.  Gaps is the potential prime locations for compared to Maximal Primes appear to be:

Gap in                                   following             Maximal               *If using a gap of 1 between 2 or 3
Potential Prime                 prime                    prime gap*         use higher value.
Locations
11                                           360653                  95 or 96
12                                           370261                  111 or 112
13                                           1349533                117 or118
And a few more up through
67                                           191912783           247 or 248

Is there any validity here?  Worth examination?  Help from someone will definitely be needed as I have gone about as far as reasonable by doing everything by hand and spreadsheet.

I modified a portion of the sieve I use if anyone is interested.  Also have a preliminary comparison between using gaps in the sieve of potential prime locations and associated Maximal Prime Gaps.

Thanks for your attention.
H. Neel
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