Is 509,203 the lowest Riesel number

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 Riesel number is an odd positive integer $k$ for which $k2^n-1$ is composite for every integer $n\ge1$. Composite means greater than one and not prime. The integer $509203$ is a proved Riesel number.

Statement recorded in the supplied source.

Is $509203$ the least Riesel number? Equivalently, for every odd integer $k$ with $1<k<509203$, does some $n\ge1$ make $k2^n-1$ prime? (The remaining smaller odd value $k=1$ also fails the Riesel condition, since $2^2-1=3$.) [S2]

Short English statement

Is five hundred nine thousand two hundred three the smallest odd multiplier whose entire powers-of-two sequence minus one is composite?

Sources

• S1 ULAM.AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 9400176 (AMR-093-0176). CC BY 4.0. https://huggingface.co/datasets/ulamai/UnsolvedMath.
• S2 Wikipedia contributors, List of unsolved problems in mathematics, revision 1366636767 (2026) Number theory, Is 509,203 the lowest Riesel number. 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, A076337: Riesel numbers: odd numbers n such that for all k >= 1 the numbers n*2^k - 1 are composite., official data snapshot 693b5499c9d2 (2026) Name, definition and comments. https://raw.githubusercontent.com/oeis/oeisdata/693b5499c9d248f570dd2d979e8bd1d7eecf689b/seq/A076/A076337.seq.