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Old 2021-08-09, 17:13   #12
robert44444uk
 
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Quote:
Originally Posted by robert44444uk View Post
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
Smallest first instance gaps to find are now 366,378,390,396,402,408,414
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
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Old 2021-08-14, 07:53   #13
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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
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Old 2021-08-16, 11:53   #14
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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
This extends http://oeis.org/A052239

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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