# 383

The only known multidigit palindromic Woodall prime.

Sexy primes are such that *n* and *n* + 6 are both prime. The pair (383, 389) for example.

The first multidigit palindromic prime to appear in the decimal expansion of π. [Wu]

The sum of the first three 3-digit palindromic primes. [Vouzaxakis]

383 is the smallest p(n) such that the continued fraction expansion of [p(n)+sqrt(p(n+1))]/p(n+2) has a prime number of coefficients in its periodic portion. [Rupinski]

The smallest prime which can be represented as sum of a prime and its reversal (241 + 142 = 383). [Gupta]

383 = 6*2^6 - 1. [Noll]

The smallest palindromic Pillai prime.

Together with 191, this prime forms a palindromic Sophie Germain pair: i.e., 2(191)+1 = 383. Less known is the fact that 383 divides the Mersenne number 2^191-1. [De Geest]

383 = prime(3*8*3) + sigma(3+8+3). Note that 383 is the earliest number (coincidentally prime) with this property. [Firoozbakht]

The smallest prime of the form 383*2^n+1 is titanic.

The product of the nonzero even digits minus 1. [Silva]

An aqueous solution of hydrochloric acid boils at a higher temperature than pure water and reaches a maximum boiling (or azeotropic) point of 383 K. [Beedassy]

The sum of three consecutive balanced primes (53 + 157 + 173). [Silva]

383 = 3^5 + 1^4 + 4^1 + 1^9 + 5^3 + 9^1. Note the first six digits of the decimal expansion of π as bases and exponents. [Silva]

The ordered concatenation of all reflectable primes up to 383 is a reflectable prime. Can you find a larger example?

The smallest palindromic curved-digit-prime. [Bajpai]

The largest prime in the binary sequence 101, 1011, 10111..., 101111111. The only one which is not prime is, ironically, the 7 digit 1011111 with 5 consecutive ones. [Homewood]

1966322 has a Collatz trajectory length of 383 and its largest prime factor is 383. Are there any larger examples of this property? [Gaydos]

A prime formed by subtracting the number of digits of Mersenne Prime M22, i.e. 2,993 from the number of digits of its immediate successor M23, i.e. 3,376 [Harrison]

David Darling's *The Universal Book of Mathematics* is a 383-page book. [Olry]

Nolan Ryan holds the Major League Baseball single-season strikeout record at 383. [Enberg]