Prime gap records

[mart_r]

Originally Posted by mart_r

OK, like I said I'll start testing 29*479909#/19#+x with -3531714 < x <= -2000000.

Done.
Taking -2000000 < x < 0.

[mart_r]

Taking 0 < x < 2000000.

[mart_r]

Taking the last remaining range 2e6 <= x <= 3e6.

[mart_r]

Michiel's gap is now verified. PFGW output files from my range are attached.
Early in the verification process I also did a sieving check up to 2e11, where the remaining candidates matched with those given in post # 103 (with about 6.2% excess of course, again matching the expected number compared to a sieve depth of 1e12).

So now the Wikipedia page can be updated.

[MJansen]

Originally Posted by mart_r

Michiel's gap is now verified. PFGW output files from my range are attached.
Early in the verification process I also did a sieving check up to 2e11, where the remaining candidates matched with those given in post # 103 (with about 6.2% excess of course, again matching the expected number compared to a sieve depth of 1e12).

So now the Wikipedia page can be updated.

Thanks Mart! Appreciated!

Will change the wiki page soon

Kind regards
Michiel

[mart_r]

Glad to hear that you're still alive.
It's been getting hauntingly quiet in the prime gap search area lately.

Should you, or anyone for that matter, be in the mood for hunting down a 10M gap (a "decamegagap":), I'd suggest a cool number like 89*770881#/8907708810±x, or 1223*747529#/122307475290±x or something like that.

Meanwhile, I'm picking up some work in the 49877# area. The Cloudygo server looks kinda bored.

[Bobby Jacobs]

That is great! Prime gaps are very fun.

[rudy235]

Excuse my ignorance but are we any closer to proving maximal gaps #81 and/or #82 as first occurrences? I believe we are not talking about these, but of just maximal (first known) gaps. Some places online say yes but there is no clear indication as to when was the search made exhaustive.

[mart_r]

It doesn''t look like we're getting any closer at the moment. The discussion in this thread petered out in November, I also don't know what Craig is doing currently.
There is still a minuscule possibility (its probability was even discussed in the thread) that a maximal gap has been overlooked. So strictly speaking, the search in the interval that Craig was working on, [2⁶⁴, 2⁶⁴+2⁶⁰], was not exhaustive.

[rudy235]

Originally Posted by mart_r

It doesn''t look like we're getting any closer at the moment. The discussion in this thread petered out in November, I also don't know what Craig is doing currently.
There is still a minuscule possibility (its probability was even discussed in the thread) that a maximal gap has been overlooked. So strictly speaking, the search in the interval that Craig was working on, [2⁶⁴, 2⁶⁴+2⁶⁰], was not exhaustive.

Yes i agree. The only thing tangible is the the first known occurrences of 1552 and 1572 now belong to Craig.

On top of that (and this is only an educated guess) both gaps will be eventually be found to be first occurrences and gap #82 will probably have the highest merit of all gaps verified as first occurrences. (at that time)

[MJansen]

Originally Posted by mart_r

Glad to hear that you're still alive.
It's been getting hauntingly quiet in the prime gap search area lately.

Should you, or anyone for that matter, be in the mood for hunting down a 10M gap (a "decamegagap":), I'd suggest a cool number like 89*770881#/8907708810±x, or 1223*747529#/122307475290±x or something like that.

Meanwhile, I'm picking up some work in the 49877# area. The Cloudygo server looks kinda bored.

Hi Mart,

just edited the wiki prime gap page. Thanks again for verifying and good luck hunting big gaps!

Ps why the fascination with the very large dividers? For me they seem too much of a (very rare) hit or (usual) miss, and after sieving and PRP-ing these huge numbers, it is rather annoying not having anything to show for ;-)

Kind regards
Michiel