Are there infinitely many Pierpont primes

Definitions and mathematical statement

Shared notation.

$\mathbb N=\{1,2,\ldots\}$, and $\mathbb Z,\mathbb Q,\mathbb R,\mathbb C$ denote the integers, rationals, reals and complex numbers. Any other conventions are specified locally.

A Pierpont prime is a prime $p$ of the form $p=2^a3^b+1$ for integers $a,b\ge0$. Equivalently, $p-1$ has no prime divisors other than $2$ and $3$; the empty factorization $p-1=1$ is allowed.

Statement recorded in the supplied source.

Are there infinitely many primes of this form? [S2]

Short English statement

Are there infinitely many primes one more than a product of powers of two and three?

Sources

• S1 ULAM.AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 9400157 (AMR-093-0157). CC BY 4.0. https://huggingface.co/datasets/ulamai/UnsolvedMath.
• S2 Wikipedia contributors, List of unsolved problems in mathematics, revision 1366636767 (2026) Number theory, Are there infinitely many Pierpont primes. https://en.wikipedia.org/w/index.php?title=List_of_unsolved_problems_in_mathematics&oldid=1366636767#Number_theory.
• S3 OEIS Foundation and contributors, The On-Line Encyclopedia of Integer Sequences, A005109: Class 1- (or Pierpont) primes: primes of the form 2^t*3^u + 1., official data snapshot 693b5499c9d2 (2026) Name, definition and comments. https://raw.githubusercontent.com/oeis/oeisdata/693b5499c9d248f570dd2d979e8bd1d7eecf689b/seq/A005/A005109.seq.