509,203

Short description: Natural number

← 509202 509203 509204 →
List of numbers — Integers ← 100 101 102 103 104 105 106 107 108 109
Cardinal	five hundred nine thousand two hundred three
Ordinal	509203rd (five hundred nine thousand two hundred third)
Factorization	prime
Divisors	1, 509203
Greek numeral	$\stackrel{\nu }{\mathrm{M}}$͵θσγ´
Roman numeral	DIXCCIII
Binary	11111000101000100112
Ternary	2212121111013
Quaternary	13301101034
Quinary	1122433035
Senary	145252316
Octal	17424238
Duodecimal	20681712
Hexadecimal	7C51316
Vigesimal	33D0320
Base 36	AWWJ36

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

In mathematics

509203 is the 42228th prime number, and an deficient number. It is conjectured to be the smallest odd number not of the form $2^n+p$ with positive or negative prime.

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, but whether it is the smallest Riesel number, it is still unproven, since there is a debate on proving or disproving whether that $k=509203$ is the smallest Riesel number. This is known as the Riesel problem, or Riesel conjecture.

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

To check if there are $k<509203$, 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. 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