The nth Prime Page will now find any of the first 2.623˙1015 primes or π(x) for x up to 1017.
The Mir Space Station docked with 31 spacecraft during its history.
31 is the third Mersenne prime.
Portal 31 is Kentucky's first exhibition coal mine.
The minimal number of moves required in a Tower of Hanoi puzzle containing five discs. The general solution to this puzzle requires a Mersenne number (i.e., 2^n - 1) of moves, where n is the number of discs.
31 = 22 + 33. [Kulsha]
(31) is prime. [Millard]
The only known Mersenne emirp.
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.
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]
California was the 31st state to be granted statehood. Hence, the U. S. flag was changed to display 31 stars and 13 stripes (an emirp pair). [Green]
((((31))))=2 is prime, (((31)))=3 is prime and ((31))=5 is prime. [Olsen]
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]
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]
The reverse concatenation of first two triangular numbers is prime. [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]
Jackson Pollock's One: Number 31, 1950 occupies an entire wall by itself at the Museum of Modern Art, New York City. The painting is oil and enamel on unprimed canvas. (Studies have shown that some of Pollock's works display the properties of fractals.)
(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]
(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 sum of digits of all primes less than or equal to 31 is prime. [Patterson]
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.
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]
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 after the decimal point are all nonzero. [Keith]
The only two-digit prime that yields an emirp if the next prime is sandwiched between its digits: 3371. [Silva]
The smallest Gaussian emirp. [Loungrides]
In the movie 2010, the code to destruct HAL is to enter 999, square root, and press integer on a calculator. That gives 31. [McCranie]
31111111111111111111111111111111/31 is prime. The numerator has 31 1's. [Firoozbakht]
The largest known prime number such that the digits of its square are in descending order. [Capelle]
Steve Homewood from England discovered that the formula 2n^2 + 4n + 31 generates prime numbers over 43 percent of the time for all positive values up to 10 million, thus solving the Alpha31 problem posed by Vasilios Gardiakos.
The largest known prime number p such that the decimal expansion of 3p does not contain any zero. [Capelle]
The smallest power of 2 with a pandigital factorization: 536870912 * 4 = 2^31. [Post]
The number of primes that were investigated by Dick Sietz in his "Prime List of Primes" that appeared in the Virginia Mathematics Teacher (Vol. 30, No. 2, 2004).
On Landon Curt Noll's web page, "The English Name of a Number," he states that: With the following 31 words, we (are) able to count up to 999999999: zero one two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen sixteen seventeen eighteen nineteen twenty thirty forty fifty sixty seventy eighty ninety hundred thousand million. [Green]
The smallest of three consecutive primes, (31, 37, 41), such that the product of the first two plus 1 is divided by the 3rd. Note that it is the largest known such case. [Loungrides]
31 = (25-1)/(2-1) = (53-1)/(5-1) = (63+1)/(6+1). [Ordowski]
There are exactly thirty-one 8-digit strobogrammatic primes: 10069001, 10911601, 11069011, 11096011, 11869811, 11896811, 16069091, 16188191, 16811891, 16900691, 16969691, 16996691, 18611981, 18688981, 19188161, 19811861, 60088009, 60611909, 60800809, 61096019, 61669919, 61696919, 61969619, 66169199, 66896899, 66911699, 68669989, 68811889, 68969689, 69800869, 69911669.
First occurrence of a run of exactly 31 consecutive integers with an even number of prime factors has never been found.
Just two 1st-move pairs in a chess game yield a maximum of 31 legal 2nd-move options for White: White's double advance of King's Pawn followed by either of 2 double advances resulting in an option to capture. [Merickel]
(There are 30 curios for this number that have not yet been approved by an editor.)
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