QUADRUPLET PRIMES AND THEIR GAPS - Page 3

robert44444uk · 2020-01-08, 17:22

Now at 1.4e14 and still no 52048. The next low numbers are 52102, 53836.

The largest gaps are

Code:

162830 55341128536691
170635 135444915341621
195044 92944027480721

Thomas11 · 2020-01-09, 12:52

Quote:

Originally Posted by robert44444uk

The largest gaps are

Code:

162830 55341128536691
170635 135444915341621
195044 92944027480721

Note that the Perl scripts for manipulating the gap results use a "hard coded" upper limit of 200000 for the gap length. So you'll need to adjust this, once you find even larger gaps.

robert44444uk · 2020-01-10, 08:47

Quote:

Originally Posted by robert44444uk

Now at 1.4e14 and still no 52048. The next low numbers are 52102, 53836.

No change at 2e14. All of the low unfound values are still there. Biggest gaps so far:

Code:

162830 55341128536691
163212 172271073415871
164543 142566888001841
169106 196472319482471
170635 135444915341621
175448 165701382062261
177027 179264456865881
180082 175934192636591
195044 92944027480721

Onwards and upwards!

pinhodecarlos · 2020-01-10, 22:18

Running from 5e14 to 8e14.

pinhodecarlos · 2020-01-11, 07:48

Quote:

Originally Posted by pinhodecarlos

Running from 5e14 to 8e14.

Meant 5e14 to 9e14.

rudy235 · 2020-01-11, 18:11

Perhaps we should try to define a column of "merit" for the gaps between Quadruplet Primes.

According to Hardy-Littlewood, we would expect a density of Quadruplets consistent with this Formula:

=4.151180864…∫2𝑁𝑑𝑥′/(log𝑥′)4

(Integral Logarirthm from 2 to x)

Bobby Jacobs · 2020-01-11, 20:54

I find it interesting that a lot of the first instances of the small gaps are just over 1000000. Out of 11 possible gaps from 1 to 15, there are 5 gaps that have the first occurrence between 1000000 and 1200000.

rudy235 · 2020-01-11, 21:28

Quote:

Originally Posted by Bobby Jacobs

I find it interesting that a lot of the first instances of the small gaps are just over 1000000. Out of 11 possible gaps from 1 to 15, there are 5 gaps that have the first occurrence between 1000000 and 1200000.

Actually 6 exceed 1,000,000 {1,4,6,10,14,15} but between 1 e6 and 1.2 e6 there are only 5

rudy235 · 2020-01-12, 01:15

Actually 6 exceed 1,000,000 {1,4,6,10,14,15} but between 1 e6 and 1.2 e6 there are only 4

pinhodecarlos · 2020-01-12, 07:42

Robert, can you please post by eob tomorrow your gaplist.txt file. This will allow me to run the script update on your latest file.

robert44444uk · 2020-01-12, 08:49

Quote:

Originally Posted by pinhodecarlos

Robert, can you please post by eob tomorrow your gaplist.txt file. This will allow me to run the script update on your latest file.

There's not a lot of point until I reach 5e14, otherwise we will not be recording first instance gaps.

I reached 3e14 this morning, so I expect to get to 5e14 sometime on Tuesday, and I'll post then.

In the meanwhile, at 3e14, the smallest non-recorded gap is still 52048, and the next few also the same, 52102, 53836.

Largest gaps are now

Code:

180082 175934192636591
180083 246762443994551
180267 228767376933281
181948 228186907139291
188433 284010274084541
195044 92944027480721

2020-01-08, 17:22	#23
robert44444uk Jun 2003 Oxford, UK 2²·13·37 Posts	Now at 1.4e14 and still no 52048. The next low numbers are 52102, 53836. The largest gaps are Code: 162830 55341128536691 170635 135444915341621 195044 92944027480721

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
GAPS BETWEEN PRIME PAIRS (Twin Primes)	rudy235	Prime Gap Searches	227	2021-01-21 21:59
Gaps between maximal prime gaps	Bobby Jacobs	Prime Gap Searches	52	2020-08-22 15:20
Prime Quadruplet Emirps	Trejack	Puzzles	11	2016-04-22 19:27
Gaps of Primes?	PawnProver44	Miscellaneous Math	10	2016-04-10 19:32
Top-5 prime quadruplet found	gd_barnes	Riesel Prime Search	10	2007-10-27 01:54

2020-01-10, 22:18	#26
pinhodecarlos "Carlos Pinho" Oct 2011 Milton Keynes, UK 1301₁₆ Posts	Running from 5e14 to 8e14.

2020-01-11, 18:11	#28
rudy235 Jun 2015 Vallejo, CA/. 973₁₀ Posts	Perhaps we should try to define a column of "merit" for the gaps between Quadruplet Primes. According to Hardy-Littlewood, we would expect a density of Quadruplets consistent with this Formula: =4.151180864…∫2𝑁𝑑𝑥′/(log𝑥′)4 (Integral Logarirthm from 2 to x)

2020-01-11, 20:54	#29
Bobby Jacobs May 2018 317₈ Posts	I find it interesting that a lot of the first instances of the small gaps are just over 1000000. Out of 11 possible gaps from 1 to 15, there are 5 gaps that have the first occurrence between 1000000 and 1200000.

2020-01-12, 01:15	#31
rudy235 Jun 2015 Vallejo, CA/. 7·139 Posts	Actually 6 exceed 1,000,000 {1,4,6,10,14,15} but between 1 e6 and 1.2 e6 there are only 4

2020-01-12, 07:42	#32
pinhodecarlos "Carlos Pinho" Oct 2011 Milton Keynes, UK 4865₁₀ Posts	Robert, can you please post by eob tomorrow your gaplist.txt file. This will allow me to run the script update on your latest file.