294,001
From HandWiki
294,001 (two hundred ninety-four thousand [and] one) is the natural number following 294,000 and preceding 294,002.
In mathematics
294,001 has only two divisors, meaning that it is the 25532nd prime number. It is also a twin prime with 293,999.[1]
Delicate Prime
294,001 is most notable for being a delicate prime in base 10,[lower-alpha 1] which is also the first one.[2][3][4][5] Since changing the number 1 in 294,001 to 7, the resulting number is divisible by 7; changing it to a 9, it becomes divisible by 3, all which are composite.[6][4]
For every , each of the numbers and , is either equal to 294001 or composite.[7][8]
Notes
- ↑ Also known as a weakly prime
References
- ↑ Vanovschi, Vitalii. "Properties of the number 294001" (in en). http://www.numberempire.com:80/294001.
- ↑ Stamm, Emily (2020) (in en). AN INVESTIGATION OF (NEARLY) WEAKLY PRIMES AND RELATED SIEVE FORMULATIONS. Unpublished. doi:10.13140/RG.2.2.24482.86723. https://www.researchgate.net/profile/Emily-Stamm-2/publication/346029641_AN_INVESTIGATION_OF_NEARLY_WEAKLY_PRIMES_AND_RELATED_SIEVE_FORMULATIONS/links/5fb7250ea6fdcc6cc64f1536/AN-INVESTIGATION-OF-NEARLY-WEAKLY-PRIMES-AND-RELATED-SIEVE-FORMULATIONS.pdf.
- ↑ Sloane, N. J. A., ed. "Sequence A050249 (Weakly prime numbers (changing any one decimal digit always produces a composite number). Also called digitally delicate primes)". OEIS Foundation. https://oeis.org/A050249.
- ↑ 4.0 4.1 Weisstein, Eric W.. "Weakly Prime" (in en). Wolfram Research, Inc.. https://mathworld.wolfram.com/WeaklyPrime.html.
- ↑ "Puzzle 17.- Weakly Primes". https://www.primepuzzles.net/puzzles/puzz_017.htm.
- ↑ Nadis, Steve (2021-03-30). "Mathematicians Find a New Class of Digitally Delicate Primes" (in en). https://www.quantamagazine.org/mathematicians-find-a-new-class-of-digitally-delicate-primes-20210330/.
- ↑ Landman, Bruce M.; Luca, Florian; Nathanson, Melvyn B.; Nešetřil, Jaroslav; Robertson, Aaron (2022-04-19) (in en). Number Theory and Combinatorics: A Collection in Honor of the Mathematics of Ronald Graham. Walter de Gruyter GmbH & Co KG. ISBN 978-3-11-075421-6. https://books.google.com/books?hl=en&lr=&id=h39sEAAAQBAJ&oi=fnd&pg=PA209&dq=294001&ots=x89dHxcBDA&sig=GuPerRH3F45DIrGxX3GvPf_GTSw#v=onepage&q=294001&f=false.
- ↑ Luckner, Thomas. "Research Statement". https://people.math.sc.edu/luckner/Research_Statement.pdf.
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