23 (twenty-three) is the natural number following 22 and preceding 24. It is a prime number.

Twenty-three is the ninth prime number, the smallest odd prime that is not a twin prime. It is, however, a cousin prime with 19, and a sexy prime with 17 and 29; while also being the largest member of the first prime sextuplet (7, 11, 13, 17, 19, 23). Twenty-three is also the next to last member of the first Cunningham chain of the first kind (2, 5, 11, 23, 47), and the sum of the prime factors of the second set of consecutive discrete semiprimes, (21, 22). 23 is the smallest odd prime to be a highly cototient number, as the solution to ${\displaystyle x-\phi (x)}$ for the integers 95, 119, 143, and 529.

Hilbert's problems are twenty-three problems in mathematics published by German mathematician David Hilbert in 1900.

The first Mersenne number of the form ${\displaystyle 2^{n}-1}$ that does not yield a prime number when inputting a prime exponent is ${\displaystyle 2047=23\times 89,}$ with ${\displaystyle n=11.}$

On the other hand, the second composite Mersenne number contains an exponent ${\displaystyle n}$ of twenty-three: $${\displaystyle M_{23}=2^{23}-1=8\;388\;607=47\times 178\;481}$$

The twenty-third prime number (83) is an exponent to the fourteenth composite Mersenne number, which factorizes into two prime numbers, the largest of which is twenty-three digits long when written in base ten: $${\displaystyle M_{83}=967...407=167\times 57\;912\;614\;113\;275\;649\;087\;721}$$

Further down in this sequence, the seventeenth and eighteenth composite Mersenne numbers have two prime factors each as well, where the largest of these are respectively twenty-two and twenty-four digits long, $${\displaystyle {\begin{aligned}M_{103}&=101\ldots 007=2\;550\;183\;799\times 3\;976\;656\;429\;941\;438\;590\;393\\M_{109}&=649\ldots 511=745\;988\;807\times 870\;035\;986\;098\;720\;987\;332\;873\\\end{aligned}}}$$

Where prime exponents for ${\displaystyle M_{23}}$ and ${\displaystyle M_{83}}$ add to 106, which lies in between prime exponents of ${\displaystyle M_{103}}$ and ${\displaystyle M_{109}}$, the index of the latter two (17 and 18) in the sequence of Mersenne numbers sum to 35, which is the twenty-third composite number.