The largest known twin prime pair each has 388,342 digits — printed at normal size, one number would run over 150 pages.

The biggest twin prime pair known to mathematics is 2,996,863,034,895 × 2^1,290,000 ± 1, two prime numbers just two apart, each 388,342 digits long.

Twin primes are pairs of prime numbers separated by exactly two — like 11 and 13, or 29 and 31. The largest such pair anyone has ever found is 2,996,863,034,895 × 2^1,290,000 − 1 and 2,996,863,034,895 × 2^1,290,000 + 1. Each of those two numbers has 388,342 decimal digits. Written out at ordinary type size, a single one of them would spill across more than 150 printed pages, and you would need both to see the pair.

The Prime Database at the University of Tennessee at Martin — the reference list mathematicians call T5K or the PrimePages — lists this pair at rank 1 in its "Twin (p)" subcategory. It is not a rounded-off estimate. The database records the exact algebraic form, and the digit count follows directly from the arithmetic: multiply a 13-digit number by 2 raised to the 1,290,000th power, and you land in the 388,342-digit range.

Who found it and how

The discovery belongs to Tom Greer, a volunteer computing for the team Sicituradastra., working inside PrimeGrid's Sophie Germain Prime Search. PrimeGrid is a distributed-computing project: instead of one supercomputer, tens of thousands of ordinary machines around the world each chew through a slice of the search. Greer's slice was crunched on an Intel Xeon E5-2623 v3 processor — a workstation chip, not exotic hardware — and the software doing the primality test was LLR, an implementation of the Lucas–Lehmer–Riesel method that is fast for numbers written in the form k × 2^n ± 1.

PrimeGrid announced the find in 2016, and The Aperiodical wrote it up the same year under the headline "New Twin Primes found," noting the pair was added to Chris Caldwell's Largest Known Primes list. That's an important detail about how mathematics polices itself here: a claim like this isn't taken on faith. The candidate is verified independently, then entered into the public T5K database where anyone can inspect the entry, check the form, and re-run the test.

The Sophie Germain search is where this gets elegant. A Sophie Germain prime is a prime p for which 2p + 1 is also prime — a structure that tends to throw off twin primes as a byproduct of the sieving. Greer wasn't hunting twins directly; the pair emerged from the machinery of a different quarry.

Why the record is so hard to break

Small twin primes are everywhere near the start of the number line. But the higher you climb, the rarer primes get, and the odds that two of them sit exactly two apart shrink faster still. To beat this record you don't just need a big prime — you need two enormous primes that happen to be neighbors, and you have to test both. This 388,342-digit pair eclipsed the previous champion of 200,700 digits, nearly doubling the record in one stroke, which is why it has stood at the top of the list for years.

One vivid way to feel the scale: the largest twin prime pair known before Greer's would have printed at roughly 80 pages per number; his runs to over 150. The gap between them is not incremental. It is a leap into territory no one had checked.

And here is the seam still open to argue about. Nobody has ever proven that twin primes go on forever. The **twin prime conjecture** — that there are infinitely many such pairs — remains unproven, though Yitang Zhang's 2013 breakthrough on bounded gaps between primes brought mathematicians closer than they'd been in a century. So every new record is a record in the most literal sense: the largest we happen to have found. Whether the pairs run out, or march on without end, is a question the arithmetic has refused to settle.