A317259 a(n) = 136926916457315893 + (n - 1)*9843204333812850.

136926916457315893, 146770120791128743, 156613325124941593, 166456529458754443, 176299733792567293, 186142938126380143, 195986142460192993, 205829346794005843, 215672551127818693, 225515755461631543, 235358959795444393, 245202164129257243, 255045368463070093

Offset: 1

Author

Marco Ripà, Jul 25 2018

Keywords

• nonn
• easy

Comments

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.

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

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

Examples

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

Links

• Jens Kruse Andersen, All known AP24 to AP26.
• B. Green and T. Tao, The primes contain arbitrarily long arithmetic progressions, Annals of Math. 167 (2008), 481-547.
• PrimeGrid, AP26 Search.
• Eric Weisstein's World of Mathematics, Prime Arithmetic Progression.
• Wikipedia, Primes in arithmetic progression.

Crossrefs

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

Programs

GAP

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

Maple

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

Mathematica

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

Extensions

a(7) corrected by Georg Fischer, Mar 13 2020