509,203

← 509202 509203 509204 →
List of numbers Integers ← 10^0 10^1 10^2 10^3 10^4 10^5 10^6 10^7 10^8 10^9 10^10 10^11 10^12 10^13
Cardinal	five hundred nine thousand two hundred three
Ordinal	509203rd (five hundred nine thousand two hundred third)
Factorization	prime
Divisors	1, 509203
Greek numeral	${\displaystyle {\stackrel {\nu }{\mathrm {M} }}}$͵θσγ´
Roman numeral	DIXCCIII, dixcciii
Binary	11111000101000100112
Ternary	2212121111013
Senary	145252316
Octal	17424238
Duodecimal	20681712
Hexadecimal	7C51316

509203 (five hundred [and] nine thousand two hundred [and] three) is the natural number following 509202 and preceding 509204.^[1]

In mathematics

509203 is the 42228th prime number, and an deficient number.^[1][2] It is conjectured to be the smallest odd number not of the form ${\displaystyle 2^{n}+p}$ with positive or negative prime.^[3]

Reisel number

Unsolved problem in mathematics

Is 509,203 the smallest Riesel number?

More unsolved problems in mathematics

509203 is most notable for being a Riesel number, specifically the smallest known one,^[4][5] but whether it is the smallest Riesel number, it is still unproven, since there is a debate on proving or disproving whether that ${\displaystyle k=509203}$ is the smallest Riesel number. This is known as the Riesel problem, or Riesel conjecture.^[6]

In 1956, a Swedish mathematician named Hans Riesel showed that there are an infinite number of positive odd integer k's such that ${\displaystyle k\times 2^{n}-1}$ is composite (not prime) for every integer ${\displaystyle n>=1}$, and showed that ${\displaystyle k=509203}$ was such one.^[7][4]

To check if there are ${\displaystyle k<509203}$, the Riesel Sieve project (analogous to Seventeen or Bust for Sierpiński numbers) started with 101 candidates k. As of December 2022, 57 of these k had been eliminated by Riesel Sieve, PrimeGrid, or outside persons.^[8] The remaining 41 values of k that have yielded only composite numbers for all values of n so far tested are:

23669, 31859, 38473, 46663, 67117, 74699, 81041, 121889, 129007, 143047, 161669, 206231, 215443, 226153, 234343, 245561, 250027, 315929, 319511, 324011, 325123, 327671, 336839, 342847, 344759, 362609, 363343, 364903, 365159, 368411, 371893, 384539, 386801, 397027, 409753, 444637, 470173, 474491, 477583, 485557, 494743^[7]

References

1. Vanovschi, Vitalii. "Properties of the number 509204". www.numberempire.com. Retrieved 2026-09-17.
2. "The Positive Integer 509203". www.positiveintegers.org. Retrieved 2026-09-18.
3. L. Honaker, G.; McLean, Reginald. "509203". Prime Curios!. Retrieved 2026-09-17.
4. E. Finch-Smith, Carrie; Scottfield Groth, R. (2025). "Arbitrarily Long Sequences of Sierpiński Numbers that are the Sum of a Sierpiński Number and a Mersenne Number" (PDF). Journal of Integer Sequences. 28 (Article 25.2.4). Retrieved 2026-09-17.
5. Sloane, N. J. A. (ed.). "Sequence A101036 (Riesel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. Weisstein, Eric W. "Riesel Number". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 2026-09-17.
7. Reggie. "About the Riesel Problem". PrimeGrid. Retrieved 2026-09-17.
8. "The Riesel Problem statistics". PrimeGrid. Retrieved 2026-09-17.