# 131

This number is a prime. A rare prime of the form 2p + 3, where p is prime. [Luhn] 131 is the 32nd prime. Note that 1 + 3 + 1 = 3 + 2. The least integer such that the sum of its digits in every base B = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 is prime. [Crespi de Valldaura] Locomotive number 131 plunges off the edge of a ravine in the sci-fi movie Back to the Future Part III. The smallest mountain prime. [Pol] The sum of 2 + 3 + 4 + ... + 19 minus the sum of primes less than 19. [Trotter] The minimum prime p such that p ± 1 each has exactly 3 distinct prime factors. [Das] Iodine-131 is a radioactive isotope used in thyroid disease diagnosis and therapy. [Barnhart] The 131st Fibonacci number (1066340417491710595814572169) is the smallest Fibonacci prime which contains all the digits from 0 to 9. [Wu] The smallest multidigit palindromic prime that yields another prime by placing a 7 on both sides (as leading and trailing digits). [Russo] The sum of three two-digit primes (31 + 41 + 59) whose concatenation is the decimal expansion of π. [Silva] (2! + 1) + (3! + 1) + (5! + 1) = 131. This is equivalent to 3 + 7 + 11^2. [La Haye] 131 is the smallest prime number which is sum of primes that begin with the digit 4. Note that 41, 43 and 47 are consecutive primes. [Capelle] The smallest palindromic prime with three primes embedded (13, 3 and 31). [Necula] The nematode Caenorhabditis elegans hermaphrodite has exactly 131 cells that are eliminated by programmed cell death (apoptosis). [Haga] The smallest palindromic super-2 number, i.e., an integer n such that 2n^2 contains 2 consecutive 2s in its decimal representation. [De Geest] The sum of the first 131 non-primes is prime. [Patterson] 131 = (1^0+3^0+1^0) + (1^1+3^1+1^1) + (1^2+3^2+1^2) + (1^3+3^3+1^3) + (1^4+3^4+1^4). Note that the summands are all primes. [Silva] 131 and the next prime after it are the first pair of consecutive primes where we can find another pair of consecutive primes by concatenating each term's end digits. [Silva] The smallest prime number appearing after the concatenation of the two preceding prime numbers (113 and 127). [Capelle] The smallest palindromic prime that yields another if the sum of digits of its consecutive digits is sandwiched between each of the corresponding consecutive digits (i.e., 131 becomes 14341). [Silva] A prime Ulam number that is the sum of two consecutive Ulam numbers (62 + 69 = 131). Can you find a greater prime example? The smallest prime that is not a quiteprime. [Beedassy] The largest prime factor of the number of mountain primes is the smallest mountain prime. [Honaker] The smallest palindromic prime using two distinct digits which when interchanged forms another palindromic prime (313). Note that in both cases a new palindromic prime with a prime number of digits is generated when each digit d is repeated d times: 13331; 3331333. [Beedassy] The smallest prime that remains prime when the end digits (on both sides) are repeated once (i.e., 11311 is also prime). The smallest Honaker prime, i.e., 131 = P32, and 1 + 3 + 1 = 3 + 2. Note that the latter sum of digits corresponds to the smallest prime with prime subscript (3 = P2) added to its very (prime) subscript. [Beedassy] 131 Main is a restaurant chain in North Carolina. We recommend their slow roasted prime rib. 131 families of Coleoptera (beetles) have been described in North America. [Bartlett] The smallest prime formed from overlapping an emirp pair (13 and 31). The smallest concave prime. [Pol] 131 "Calendar Club" game stores were opened in 1999. A checking method is described to see if 131 is prime at the bottom of "Prime Factors" (a page from a Houghton Mifflin Harcourt website called Education Place). The smallest prime equidistant between two consecutive emirps: 113, 149. [Beedassy] The 1st prime after p(31) is 131. [Silva] The only palindromic prime that is the sum of the reversals of two double-digit primes, i.e., 43 and 79. [Loungrides] The statue of Genghis Khan near Ulan Bator, Mongolia, is 131-foot tall. The smallest n-digit palindromic prime with central digit n, (n=3). [Loungrides] The smallest 3-digit prime that remains prime when inserting one, two or three zeros between its digits, i.e., 10301, 1003001, 100030001 are primes. The other is 577. [Loungrides] The smallest palindromic prime equal to a prime plus the sum of all previous composite numbers, i.e., 19+18+16+15+14+12+10+9+8+6+4. [Silva] The smallest palindromic prime that is the sum of three consecutive primes (41+43+47). [Silva] Sum of the factorials of the first six Fibonacci numbers: 0!+1!+1!+2!+3!+5! = 131. [Silva] The smallest prime of form p*q-(r+s), where p, q, r, s are four consecutive primes, i.e., (13, 11, 7, 5). [Loungrides] The fifth prime whose sum of digits is 5. [Loungrides] In the James Bond movie "A View to a Kill," the check that Zorin writes for S. Sutton (for \$5,000,000) is numbered 131. Daigoro's father cut off the heads of 131 lords for the Shogun. [Post] Smallest Sophie German prime which is also an irregular prime. Smallest irregular Sophie-German prime. The smallest palindromic prime with exactly three nonzero digits. [Buddenhagaen] 131 is the smallest pallindromic prime that remains so by inserting the following same digit d six times between its adjacent digits, one at a time, for d = 0, 1, 3, 4, 6, 9 (6 times): 10301 = prime 11311 = prime 13331 = prime 14341 = prime 16361 = prime 19391 = prime. [Rivera] The sum of the first one hundred thirty one 131-digit primes is prime. Can you find a larger example like this? [Gaydos] Not only is 131 the first Honaker prime, but it's also a Sophie Germain prime whose associated safe prime is 263, the second Honaker prime. [Gaydos] The restaurant "131" (www.one-thirtyone.com) is nestled in Hong Kong's Three Fathoms Cove. It is reminiscent of a luxury European country retreat in an atmosphere that is elegant and relaxed. Abbey's Bookshop in Sydney, NSW, Australia, is located at 131 York Street. The Collatz trajectory length of 131000. [Gaydos] 131 is alphanumeric code for ACA, or Anti Communist Action. The first three-digit term to occur in Van Eck's Sequence. 131 is the sum of three two-digit primes which appear as first digits of the decimal expansion of pi: 31+41+59. [Silva] The smallest and possibly the only odd-digit palindromic prime that is partial sums of numbers (1+3+5+7+9...+31 = 131) whose divisors have only odd digits. Note that the primes with this property are 131, 199, 379, 519793, 113715733399, ... . [Sariyar] 131 can be written as the sum of three distinct prime-digit primes with distinct prime digits, i.e., 131 = 5 + 53 + 73. 131 is the smallest prime fully auto-insertable (into all of its internal positions), one at a time. Accordingly, the following two integers are primes: 1'131'31, 13'131'1 [Rivera] Italian polymath Girolamo Cardano was the author of 131 books. [Bellos] Bamboo can grow as large as 131 feet high. [Davis] 131 is the local area or city code used to dial to Edinburgh, Scotland. [Ñape]

(There are 21 curios for this number that have not yet been approved by an editor.)