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A375344
First term p1 of octuplets of consecutive prime numbers pi with given successive gaps pi-p1, i=2, ...,8 (6, 8, 18, 24, 30, 36, 38).
0
233, 2721413, 154670903, 200559053, 232777673, 273788363, 299267663, 459117353, 527326403, 1015923113, 1563572243, 1688692763, 2426018723, 2918492243, 3743134523, 4445599853, 4458163943, 4697619593, 5493835013, 5546977823, 5930389313, 6131660663, 6470661143, 7598587943
OFFSET
1,1
COMMENTS
The choice of successive gaps (6, 8, 18, 24, 30, 36, 38) is such that the sum of the eight prime numbers beginning with 233 is 2024. The next year being the sum of analogous octuplet is 21771464 (21772nd millenium).
LINKS
René-Louis Clerc and Jean-Baptiste Hiriart-Urruty, The octuplet of the year 2024 and its relatives, pp. 1-10, hal-04666530, 2024.
EXAMPLE
233, 239, 241, 251, 257, 263, 269, 271 (sum = 2024).
2721413, 2721419, 2721421, 2721431, 2721437, 2721443, 2721449, 2721451 (sum = 21771464).
PROG
(PARI) uplet(p)= {n=0; for(i=p, p+38, if(isprime(i), n+=1)); n}
octo(m)={for(p=3, p=10^m, if(isprime(p) && isprime(p+6) && isprime(p+8) && isprime(p+18) && isprime(p+24) && isprime(p+30) && isprime(p+36) && isprime(p+38) && uplet(p)==8, print1(p, ", ")))}
listocto(p1)=print1(p1, ", ", p1+6, ", ", p1+8, ", ", p1+18, ", ", p1+24, ", ", p1+30, ", ", p1+36", ", p1+38)
KEYWORD
nonn
AUTHOR
René-Louis Clerc, Aug 12 2024
STATUS
approved