# 67

This number is a prime. John Pilkins ©2003 Mersenne claimed 267 - 1 was prime, but it's composite. The smallest two-digit Hyper-Cullen 2nd species prime, i.e., a prime of the form n * 2n + (n - 1). [Russo] 6! * 7! = 10!. The largest prime which is not the sum of distinct squares. [Crespi de Valldaura] π(6*7) = 6+7. [Firoozbakht] 67 = sqrt(9!/(9 * 9) + 9). [Poo Sung] 567 starts with the digits 67. [Hartley] The hull number of the U.S. Navy's aircraft carrier USS John F. Kennedy (CV-67). The smallest prime which contains all ten digits when raised to the tenth power. [Patterson] The "Summer of Love" was a phrase given to the summer of '67, describing (personifying) the feeling of being in San Francisco that summer when the hippie movement came to full fruition. If A = 1, B = 6, C = 1, D = 8, ... , (using the digits of the Golden Ratio), then 'MARIN MERSENNE' = 67; a prime exponent that he himself believed would produce a Mersenne prime number, but which later was proved to be composite [Homewood] The inventor of natural logarithms (John Napier) died at the age of 67. *67 ("star 67") is a free phone feature that blocks sending name and phone number on an outgoing individual call. Use *67 + number being dialed (must be done for each call). [Greer] The smallest prime p that divides the number of composites less than the (p + 1)th prime. [Honaker] Using the alphabet code, the value of 67 in its Roman numeral-based representation (LXVII) is the reversal of 67. [Necula] In the opening scenes of the movie Hard Target, set in New Orleans, a horse and carriage numbered 67 rumbles by. [Haga] The Escher compound that appears in the "Waterfall" lithograph by M. C. Escher divides the three component cubes into 67 individual cells. [Post] 67 is the sum of a twin prime pair. [Rivera] Longitude 67 degrees West passes through the easternmost city in the United States (Eastport, Maine). A prime place to see the sunrise. [Punches] 2^6 + 2^1 + 2^0 = 26 + 21 + 20 = 67. [Morse] Charles Lindbergh was the 67th man to make a non-stop flight over the Atlantic Ocean. (The first were Alcock and Brown, the 31 men on the English dirigible R34, and the 33 men on Zeppelin-Airship LZ126.) [Caldwell] A new born infant is considered full-term when the gestation age in weeks lies between pk+6 and pk+7, where pk = 6+7 and pn is the nth prime (i.e., between 37 and 41 weeks). [Beedassy] The sum of all idoneal primes. (A positive integer m is idoneal if and only if it cannot be written as ab + bc + ac for integer a, b, and c with 0 < a < b < c.) [Loungrides] Fresh milk has a pH of 6.7 and is therefore slightly acidic. [O'Mahony] The largest known prime number p for which the decimal expansion of 2p does not contain any pair of consecutive equal digits. It's also the case for the decimal expansion of 3p. [Capelle] The largest known prime number p for which the decimal expansion of 2p does not contain any zero. [Capelle] Smallest multidigit prime whose square (i.e., 4489) and cube (i.e., 300763) consist of different digits. [Gupta] Smallest odd prime number of bicentered 3-valent (or boron, or binary) trees with n nodes. Here with n = 12. [Post] Any digit n, 1 through 9, times 67 yields a 3-digit number (for the purpose of this discussion make 1*67 = 067), then the concatenation of the first and last digits of the product equals n times 7. E.g., 8*67 = 536 and 8*7 = 56. [Green] "And that which the rest of the people gave was twenty thousand drams of gold, and two thousand pound of silver, and threescore and seven priests' garments." (Nehemiah 7:72, KJV) To "be at sixes and sevens" is an informal expression meaning to be thoroughly confused. [Jose] Foucault's most famous pendulum contained a 67-meter long wire. One smoot is equal to 67 inches. The only double-digit prime ab such that p^b+[R(p)]^a is prime, where R(p) is the reversal of p, i.e., 67^7+76^6 = 6253411533899. [Loungrides] The first prime midway between a square and a cube, (3^2 and 5^3). [Loungrides] AC/DC's lead singer Bon Scott died at number 67 Overhill Road, in East Dulwich, South London. [Warren] Season 8, Episode 184 of "Dr. Oz" featured a woman who claims to have 67 different personalities. [Stath] The smallest polite prime that is a concatenation of two successive polite numbers, i.e., (6=1+2+3, 7=3+4). [Loungrides] The last combat use of the Norden bombsight was in the US Navy's VO-67 squadron. The smaller of only two non-titanic primes of form n^(n-1)+(n-1) for n a composite number, (case n=4), i.e., 4^3+3. The other prime is for n=10. [Loungrides] There are 67 four-digit Lynch-Bell numbers. [Shepherd] Nisan is considered the first month of the Jewish calendar, although it occurs 6 or 7 months after the start of the calendar year. [Tøndering] The smallest positive integer whose double (134) contains a 3 and whose triple (201) contains a 2. [Gaydos] Can you solve this week's puzzle (#67) My Prime ? Rosetta and its lander called Philae tracked down a comet known as "67P" after a decade journey through space. The British Museum houses 67 Isle of Lewis Chess Pieces. [Riddle] A black hole of one solar mass (M☉) takes more than ten to the power 67 years to evaporate—much longer than the current age of the universe. [Hawking] BookAuthority rates “Prime Curios!” as one of the 67 best prime numbers books of all time, based on public mentions, recommendations, ratings and sentiment.

(There are 36 curios for this number that have not yet been approved by an editor.)