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 with positive or negative prime.
Reisel number
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 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 is composite (not prime) for every integer , and showed that was such one.
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. 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
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