twelve primes in a row, 202 digits each

twelve primes in arithmetic progression, every one of them 202 digits long. found on 7 nov 2026 and proven the same morning:

what it is

an ap-12 is twelve primes with the same gap between each one and the next. 461# is the product of every prime up to 461 (a primorial), so the gap here is 819928252·461#.

the primorial is what makes long runs possible at all. the gap of any ap-k has to be divisible by every prime up to k, or some small prime lands on one of the terms. 461# covers that many times over.

the terms

all twelve in full are in ap12_202_terms.txt. the first and last:

n=0:  1468211626072585972537322892436924257483827596252930506973047369661560180582141842997187111050847758198510884775781006786386232767225963602627122070466126321277545821582138982051875209579131194357991631
n=11: 1559328877622421115049041579621597494393507989185846740837457470993658134787204069627043785207272948027378048477654502440980317506333568635641335230028997651180188194713794383174335753633736607277529271

the proof

each term has an ecpp certificate (elliptic curve primality proving) made with andreas enge's cm, and all twelve pass its separate checker, ecpp-check. the terms at n = −1 and n = 12 are composite, so the run is exactly twelve long.

certificates (ecpp and n−1, 72kb): ap12_202_certs.zip.

the record

as of 7 nov 2026, the ap-12 on norman luhn's list of ap records and in the wikipedia table is (18280594787 + 5339736233·n)·461# + 1, 201 digits, from 7 jan 2025. this one is 202.

• ·luhn's list: pzktupel.de/PAP/aprecords.php.
• ·my 1,060-digit ap-9 is on the same list, and #1 on the prime pages ap-9 list.