16843 (number)
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|---|---|---|---|---|
| Cardinal | sixteen thousand eight hundred forty-three | |||
| Ordinal | 16843rd (sixteen thousand eight hundred forty-third) | |||
| Factorization | prime | |||
| Divisors | 1, 16843 | |||
| Greek numeral | ͵Ϛωμγ´ | |||
| Roman numeral | XVMDCCCXLIII, xvmdcccxliii | |||
| Binary | 1000001110010112 | |||
| Ternary | 2120022113 | |||
| Senary | 2055516 | |||
| Octal | 407138 | |||
| Duodecimal | 98B712 | |||
| Hexadecimal | 41CB16 | |||
16843 (sixteen thousand eight hundred [and] forty-three) is the natural number following 16842 and preceding 16844.
In mathematics
[edit]16843 is the 1944th prime number.[1] It is also a prime such that the next n successive differences are identical.[2]
For , one of the irregular pairs of various forms is for .[3]
Wolstenholme prime
[edit]16843 is the first and smallest of only two known Wolstenholme primes, the other which is 2124679.[4][5][6] In the latest search for Wolstenholme primes in 2007, the authors Richard J. McIntosh and Eric L. Roettger stated that there are no more existence of Wolstenholme primes less than 10^9.[7][6][4]
References
[edit]- ↑ Vanovschi, Vitalii. "Properties of the number 16843". www.numberempire.com. Retrieved 2026-09-11.
- ↑ Sloane, N. J. A. (ed.). "Sequence A087562 (Primes such that the next n successive differences are identical)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Weisstein, Eric W. "Irregular Pair". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 2026-09-11.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A088164 (Wolstenholme primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Weisstein, Eric W. "Wolstenholme Prime". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 2026-09-11.
- 1 2 Carofiglio, Leonardo; De Filpo, Luigi; Gambini, Alessandro (June 2024). "p-adic valuation of harmonic sums and their connections with Wolstenholme primes" (PDF). Indian Journal of Pure and Applied Mathematics. 55 (2): 555–566. doi:10.1007/s13226-023-00387-1. ISSN 0019-5588.
- ↑ McIntosh, Richard; Roettger, Eric (2007-04-17). "A search for Fibonacci-Wieferich and Wolstenholme primes". Mathematics of Computation. 76 (260): 2087–2094. doi:10.1090/S0025-5718-07-01955-2. ISSN 1088-6842.
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