509,203
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|---|---|---|---|---|
| Cardinal | five hundred nine thousand two hundred three | |||
| Ordinal | 509203rd (five hundred nine thousand two hundred third) | |||
| Factorization | prime | |||
| Divisors | 1, 509203 | |||
| Greek numeral | ͵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
[edit]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 with positive or negative prime.[3]
Reisel number
[edit]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 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 is composite (not prime) for every integer , and showed that was such one.[7][4]
To check if there are , 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
[edit]- 1 2 Vanovschi, Vitalii. "Properties of the number 509204". www.numberempire.com. Retrieved 2026-09-17.
- ↑ "The Positive Integer 509203". www.positiveintegers.org. Retrieved 2026-09-18.
- ↑ L. Honaker, G.; McLean, Reginald. "509203". Prime Curios!. Retrieved 2026-09-17.
- 1 2 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.
- ↑ Sloane, N. J. A. (ed.). "Sequence A101036 (Riesel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Weisstein, Eric W. "Riesel Number". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 2026-09-17.
- 1 2 Reggie. "About the Riesel Problem". PrimeGrid. Retrieved 2026-09-17.
- ↑ "The Riesel Problem statistics". PrimeGrid. Retrieved 2026-09-17.
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