A317259 - OEIS

%I #12 Mar 13 2020 17:54:48

%S 136926916457315893,146770120791128743,156613325124941593,

%T 166456529458754443,176299733792567293,186142938126380143,

%U 195986142460192993,205829346794005843,215672551127818693,225515755461631543,235358959795444393,245202164129257243,255045368463070093

%N a(n) = 136926916457315893 + (n - 1)*9843204333812850.

%C The terms for n = 1..26 are prime. As of Jul 25 2018, this is one of the longest known sequences of primes in arithmetic progression.

%C a(27) = 392850229136449993 = 41 * 179 * 53529122378587.

%C To date, an arithmetic sequence of 27 primes has not been found yet.

%H Jens Kruse Andersen, <a href="http://primerecords.dk/aprecords.htm#ap24">All known AP24 to AP26</a>.

%H B. Green and T. Tao, <a href="http://arxiv.org/abs/math.NT/0404188">The primes contain arbitrarily long arithmetic progressions</a>, Annals of Math. 167 (2008), 481-547.

%H PrimeGrid, <a href="http://www.primegrid.com/download/AP26.pdf">AP26 Search</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeArithmeticProgression.html">Prime Arithmetic Progression</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Primes_in_arithmetic_progression">Primes in arithmetic progression</a>.

%e a(26) = 136926916457315893 + 25*44121555*223092870 = 383007024802637143 is prime.

%p seq(136926916457315893+(n-1)*9843204333812850,n=1..25);

%t Table[136926916457315893 + (n - 1) 9843204333812850, {n, 1, 25}]

%o (GAP) List([1..25], n->136926916457315893+(n-1)*9843204333812850);

%Y Cf. A002120, A204189, A260751, A261140, A317163, A317164.

%K nonn,easy

%O 1,1

%A _Marco Ripà_, Jul 25 2018

%E a(7) corrected by _Georg Fischer_, Mar 13 2020