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31 (another Prime Pages' Curiosity) |
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times on that day (and possibly the next). (caldwell@utm.edu)
 3 is close to 31. [Luhn]
The Mir Space Station docked with 31 spacecraft during its history. 31 is the third Mersenne prime. The number of letters (in English) required to write the word names of the first six primes is the sixth prime reversed, i.e., 31. [Trotter] There are only 31 numbers that cannot be expressed as the sum of distinct squares. Portal 31 is Kentucky's first exhibition coal mine. 31 = (2 * 3 * 5) + 1 or 5# + 1.
31 + the floor function of The number of moves required in a Tower of Hanoi Puzzle containing five discs. The general solution to this puzzle requires a Mersenne number of moves, where n is the number of discs. The smallest multidigit prime with an odd period length. Mersenne prime M(31) could easily be confused with our nearest large neighbor galaxy Andromeda, i.e., M31 (or Messier 31). 31 = 22 + 33. [Kulsha] The smallest prime whose digits are reversed in base 28. [Haga] The smallest prime such that replacing each digit d with d copies of the digit d produces a different prime (3331).
There are 31 milligrams of cholesterol in a tablespoon of butter. 312 = 961 and 169 = 132. The only known Mersennemirp. The smallest prime which is the sum of two Smith numbers (4 + 27). 31 = -1 + 23 * 4, demonstrating four basic arithmetic operations. [Kulsha] The speed limit in downtown Trenton, a city in western Tennessee, is 31 miles per hour. 31 divides 311 + 312 + 313 + ... + 3130 + 3131 a prime number of times. [Luhn] 31 letters of the Russian alphabet are pronounceable. 3 + 5 + 7 + 11 + ... + 89 = 312, and the sum of the first 31 odd primes is a perfect square. Paul Dirac predicted antimatter and won a Nobel Prize in 1933 (a prime). Carl Anderson detected antimatter and won a Nobel Prize three years later. Both men were age 31 when they won the Nobel Prize, and they tie for being the youngest Nobel laureates. [McCranie] There are 31 pairs of spinal nerves in the human body. [Beedassy] In the Cambridge segment of Crown & Country TV series, KQED, hosted by Edward Windsor, it was noted that Cambridge University eventually consisted of 31 colleges. [Haga] The sum of digits of the 31st Fibonacci number is 31. [Gupta] 31 is the largest primorial prime less than the next prime squared, i.e., 5# + 1 = (2*3*5) + 1 = 31 < 72 = 49. [Nicholson]
3 + 1 = 4 and (4!/.4 + sqrt(4))/sqrt(4) = 31. [Hoge] The big "31" sign made its debut at all Baskin-Robbins stores in 1953, offering customers a different ice cream for every day of the month. Note that 31 is the largest prime factor of 1953. [Coneglan] 31 is a prime number equal to the sum of the decimal digits of its 7th power (317 = 27512614111, which sums to 31). [Keith] The first chapter of the Bible has 31 verses. [Silva] The first U.S. space satellite (Explorer-I) weighed just less than 31 pounds and was launched on Jan 31, 1958. The high-power transmitter worked for 31 days. [McCranie] (2^31-1)/(2-1) and (2^31+1)/(2+1) are both prime numbers. [Dobb] The prime number 31 is also a repunit in three different bases: 31 is 11111 in base 2; it is 111 in base 5, and it is 11 in base 30. [Dobb] 31 and the 31st prime are both Mersenne primes. [Wu] The smallest multidigit quintan prime: p = (x^5 - y^5 )/(x - y). [Russo] Buddha preached on the 31 levels of existence in our universe. [Jen] 31 is the smallest multi-digit prime in the decimal expansion of cube root of 31. [Gupta] If t(n) represents the nth triangular number, then 31 is the smallest prime of the form t(p) + t(q), where p and q are themselves prime. [Rupinski] The smallest prime which is a generalized repunit in three different bases. [Rupinski] The largest integer such that the average number of triangular numbers required to express the integers less than or equal to it is exactly two. [Rupinski] The reverse concatenation of first two Triangular numbers is prime. [Gupta] 31 squared when turned upside down is a perfect square. [Friend] The smallest prime that can be represented as the sum of two triangular numbers in two different ways (21 + 10 and 28 + 3). [Gupta] For any 200560490130 consecutive whole numbers on the number line, exactly 1021870080 will have the number 31 for a lowest prime factor. [Schuler] 7 + 11 + 13 = 31. [La Haye] The Book of Proverbs has 31 chapters. This is the largest prime number of chapters for any book of the Bible. [Hartley] The earliest and the only known case such that the sum of the divisors of two distinct numbers (16 & 25) is the same prime quantity (31), that is to say: 1+2+4+8+16 = 31; 1+5+25 = 31. [Rivera] (3131 - 1)/(31 - 1) is prime. [Capelle] 3^31 - 2^31 is prime. [Capelle] The smallest prime p such that neither 6p-1 nor 6p+1 are primes. [Necula] The number of regular polygons with an odd number of sides that can be constructed with straightedge and compass. (31^31-1)/30 is prime and the largest known generalized repunit prime, where b = n. Lance Armstrong, in 2003 (at the age of 31), became the 2nd person ever to win the Tour De France 5 times consecutively, beating the runner-up Jan Ullrich by 61 seconds. Note that 2, 5, 31, 61, and 2003 are all prime numbers. [Hartley] The prime number 31# + 1 has sum of digits equal to 31. [Gallardo] The sum of digits of all primes less than or equal to 31 is prime. [Patterson] In the Star Trek episode "Terra Prime," Reed's Section 31 contact provides information to help the Enterprise crew infiltrate a Martian colony. After removing two opposing corner squares on a chessboard it is impossible to arrange 31 dominoes in such a way that they cover all the remaining squares. A computer analysis by Ströhlein and Zagler shows that the winning process in a Queen versus Rook endgame should take at most 31 moves. Frank Leon Drew was the senior supervising engineer on the Hooker 100" telescope which was the largest telescope in the world for 31 years. [McGown] Moser's circle problem asks to determine the most pieces into which a circle is divided if n points on its circumference are joined by chords with no three internally concurrent. The first few values are 1, 2, 4, 8, and 16. What do you think the next term will be? [Post] If a rhombic tricontahedron is properly numbered with ascending and descending ordered number pairs, then each sum of the individually opposite paired sides is 31. [McGown] Ben Johnston is known for composing music based on a flexible tuning system that derives pitches from as high as the 31-limit. The "prime limit" of an interval or chord in just intonation is the largest prime number in its factorization. Time dilation remained an unproved theory for 31 years after it was first proposed by Albert Einstein. [Wilson]
31 is the largest integer n such that the first n digits of The only two-digit prime that yields an emirp if the next prime is sandwiched between its digits: 3371. [Silva]
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