# 191

This number is a prime.

The smallest palindromic prime of the form *n* * phi(*n*) - 1. [Russo]

The reversal of fib(191) is prime.

If A=1, B=2, C=3, ..., Z=26, then "PALINDROMES ARE FUN" = 191. [Strachan]

The last three digits of M(11213). [Griffin]

A prime number of spaces are formed if we choose *n* = 191 distinct points on a circle so that no three of the chords that join them are concurrent. In general, the number is *g*(*n*) = (*n*^4 - 6*n*^3 + 23*n*^2 - 18*n* + 24)/24.

The Major League Baseball record for most runs batted in (RBIs) in a single season is 191, set by Hack Wilson of the Chicago Cubs in 1930. [Litman]

American Airlines Flight 191, which crashed on May 25, 1979, remains the deadliest airplane accident on U.S. soil in terms of the total number of aircraft occupants killed.

The smallest multidigit palindromic prime that yields a palindrome when multiplied by the next prime: 191 * 193 = 36863. [Russo]

191 is the smallest prime such that the sum of the reciprocals of the primes less than or equal to it begins with the digits of the next prime. Thus, 1/2 + ... + 1/191 = 1.9337.... [Rupinski]

149 and 191 are both prime. So are both 149*2^191+1 and 191*2^149+1. [Hartley]

The larger of the first occurrence of two successive primes using no prime digits. [Murthy]

When the palindromic prime 191 is doubled and one is added to this result, the resulting number is yet another palindromic prime. [Dobb]

The values of the most popular United States coins currently in circulation (silver dollar, half-dollar, quarter, dime, nickel, and penny) sum to 191 cents. [Patterson]

The smallest palindromic prime *p* such that neither 6*p* - 1 nor 6*p* + 1 is prime. [Necula]

The smallest palindromic prime whose sum of digits is a multidigit palindromic prime. [Gallardo]

Multiply the even composites 4*6*8 - 1 and get 191 using 3 terms and 2 multiplications. Do the same + 1 and get 193 -- the first set of twin primes using this process. [Haga]

191 has a prime number (19) of letters in its English name "ONE HUNDRED NINETY-ONE." Note that 191 contains 19 if read from the right or left. [Post]

The smallest prime in a set of four consecutive multidigit primes, i.e., {191, 193, 197, 199}, whose sum of digits, i.e. {11, 13, 17, 19} is another set of four consecutive primes. [Gupta]

A palindromic prime whose square is a distinct-digit number whose first two digits, central digit, and last two digits, are perfect squares.

There are 191 orientable octahedral manifolds. [Beedassy]

This number turned upside down forms the first three digits in the decimal expansion of the golden ratio (phi = 1.618...). [Meiburg]

The number of RBIs by baseball player Hack Wilson in the 1930 season, which is still a record today. [Homewood]

First member of a pair of Sophie Germain primes which are palindromic: 191*2+1 = 383. [Silva]

The smallest prime to have no single digit primitive roots. [Ewing]

The prime quadruplet {191, 193, 197, 199} has sums of digits {11, 13, 17, 19}, that is the first multi digit prime quadruplet. [Loungrides]

x! + 191 is prime, where x = 2, 3, 5, 7 and 11. [Loungrides]

The smallest prime number in the smallest prime decade in which the product of the four prime numbers is a reverse prime. [Gaydos]

The lesser in the largest known twin prime pair of the form n*2^(n-1) +/- 1. [Honaker]

191 is the sum of the first 19 integers plus 1. [Silva]

The smallest prime number that falls between two happy numbers. [Gaydos]

Question: What is the only prime whose square has five different digits that contain an even square digit in the middle with the first and last pairs being squares as well? Answer: 191. [Friend and Honaker]

(191, 251) is the only pair of 3-digit primes that can be represented as the product of two consecutive primes minus their sum, and to the product of the same primes plus their sum, 13*17 - (13+17) = 191, 13*17 + (13+17) = 251. Note that the concatenations in both orders of the elements of this pair, i.e., 191251 and 251191 are both primes. [Loungrides]

191 is the smallest prime that is a semiprime when turned upside down. [Honaker]

191 lucky numbers each have the same number of digits as its lucky index. [Gaydos]

Shigeru Kondo and Alexander Yee ran a custom-built computer for 191 days to calculate π to ten trillion decimal places. [Jackson]

Crockett Johnson based his painting Proof of the Pythagorean Theorem [Euclid] on a diagram in Ivor
Thomas’s article on Greek mathematics in *The World of
Mathematics* edited by James R. Newman (on page 191).

The smallest prime absent in the first 1000 digits of irrationals π, e and sqrt(2). [Rivera]

The sum of the digits of the first (1+9+1) primes with a digit-9 up to an including 191 equals the (1*9*1)th such prime. [Worrom]

Zero appears 191 times in the first one thousand primes. [Haga]

191 is the larger member of the smallest "Dolly Parton prime pair"; where working (changing) 9 to 5 produces a smaller prime number, i.e., 151. [Jenkins]

Palindromic prime sum of arrangements for one thru four circles in the affine plane, i.e., 1 + 3 + 14 + 173 = 191. [Wiszowaty]