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 robert44444uk 2021-08-09 17:13

[QUOTE=robert44444uk;584684]Tested now up to 4.1e14 and a first gap of 420 has appeared!

New first instance double gaps:

[CODE]

203340719517647 203340719517989 203340719518331 342
227795281925129 227795281925483 227795281925837 354
130520768860387 130520768860747 130520768861107 360
269099493634513 269099493634897 269099493635281 384
187891466722493 187891466722913 187891466723333 420[/CODE]

Smallest first instance gaps to find are now 366,378,390,396,402,408,414[/QUOTE]

I'm up to 8.3e14 and taking this through to 1e15. 420 was repeated in the range just checked, but with no other 400's

New first gaps:

[CODE]
700926505323491 700926505323857 700926505324223 366
829317525163213 829317525163591 829317525163969 378
[/CODE]

 robert44444uk 2021-08-14 07:53

I completed the CPAP 3s up to 1e15, where I will stop. There were no further first instance examples to report. The largest examples in the range 87e13 to 100e13 were a pair of 378s.

I'm looking now at CPAP 4 and CPAP 5s, with a view to taking each to 1e15. At present I am at approx 2e13.

I have already found this unknown first instance beauty CPAP 5, all prime, all are separated by 120 all intervening integers are composite.

6683799874901 6683799875021 6683799875141 6683799875261 6683799875381

The first instance CPAP 5 30s and 60s were known, but not the first instance 90

112740413623 112740413713 112740413803 112740413893 112740413983

 robert44444uk 2021-08-16 11:53

Some CPAP 4 results to 1e14, first instance gaps (which are multiples of 6) I found found are as follows:

[CODE]
144 2988385487729 2988385487873 2988385488017 2988385488161
150 2665078848911 2665078849061 2665078849211 2665078849361
156 2867966168491 2867966168647 2867966168803 2867966168959
162 15559179029347 15559179029509 15559179029671 15559179029833
168 6213483902443 6213483902611 6213483902779 6213483902947
174 10435932748939 10435932749113 10435932749287 10435932749461
180 16006204702031 16006204702211 16006204702391 16006204702571
186 53461936795321 53461936795507 53461936795693 53461936795879
192 84217066456967 84217066457159 84217066457351 84217066457543
198 55463759865203 55463759865401 55463759865599 55463759865797
204 15178802276249 15178802276453 15178802276657 15178802276861
210
216
222 52418103824077 52418103824299 52418103824521 52418103824743

[/CODE]

This extends [URL="http://http://oeis.org/A052239"]http://oeis.org/A052239[/URL]

it is notable there are no 210 gap CPAP 4s in the range from 2 to 1e14 - a requirement for CPAPs larger than CPAP 6 is that all gaps must be a multiple of 210.

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