1093 (number)

← 1092 1093 1094 →
List of numbers — Integers ← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →
Cardinal	one thousand ninety-three
Ordinal	1093rd (one thousand ninety-third)
Factorization	prime
Divisors	1, 1093
Greek numeral	,ΑϞΓ´
Roman numeral	MXCIII
Binary	100010001012
Ternary	11111113
Quaternary	1010114
Quinary	133335
Senary	50216
Octal	21058
Duodecimal	77112
Hexadecimal	44516
Vigesimal	2ED20
Base 36	UD36

1093 (one thousand [and] ninety-three) is the natural number following 1092 and preceding 1094.

In mathematics

1093 has only two divisors, meaning that it is the 183rd prime number. It is also a twin prime with 1097, a repdigit in ternary, the smallest 4-digit star prime, and a centered dodecagonal number. It is part of the Moser-de Bruijn sequence since it is the sum of distinct power of 4, and the Flavius Josephus's sieve.

1093 + 4, and (1093 + 1)/2 is prime.

Wieferich prime

1093 is most notable for being the first, and smallest out of only two known Wieferich primes, since $1093^2$ divides $2^{(1093-1)}-1$, or such that $2^{1093-1}\equiv 1(\mathrm{mod}2)$, which is similar to the Fermat's little theorem. A Wieferich prime is named after Arthur Wieferich, although Wieferich himself found no example of a prime, but in the year 1913, W. Meissner discovered 1093 as a Wieferich prime.

In other fields

• The book Mathematics: From the Birth of Numbers by Jan Gullberg contains a titanic prime of 1093 pages.

• Thomas A. Edison held 1093 successful patent applications in the United States.

References

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