# 97

This number is a prime. Carla Kik © 2004 Pub 97 in Groveland, Massachusetts, serve 97 different kinds of burgers. [Homewood] The last two digits of Jack Reacher's ATM card PIN in the novel Bad Luck and Trouble by Lee Child. Reacher liked 97 because it is the largest two-digit prime number. [Reynolds] The smallest odd non-cluster prime. An odd prime p is called a cluster prime if every even positive integer less than p-2 can be written as the difference of two primes q - q', where q, q' is less than or equal to p. The number formed by the concatenation of odd numbers from one to 97 is prime. [Howell] There are 97 leap days every four hundred years in the Gregorian calendar. [Poo Sung] Physiology is reduced to the economic needs of locomotion at the prime number tempo of 97 beats per minute. [Hayes-Marshall] The smallest prime comparable to all minimal primes in base 3. [Rupinski] The largest known prime which can be expressed as the sum of equal powers of two consecutive primes (i.e., 2^4 + 3^4). [Gupta] There are 97 chapters, some as short as a paragraph or two, in Bruce Chatwin's book In Patagonia, giving the entire book a vignette-like feel. [Deemikay] Shakespeare's Sonnet XCVII (97) has a curious property. The seventh word of the seventh line of the sonnet is "prime." [Keith] 97, 907, 9007, 90007 and 900007 are all primes, but 9000007, 90000007, 900000007, 9000000007, and 90000000007 are all composites. The smallest prime which is the sum of a prime number of consecutive primes as well as the sum of a composite number of consecutive composite numbers: 97 = 29 + 31 + 37 = 22 + 24 + 25 + 26. [Beedassy] The smallest prime that has a prime alphabetic value in its Roman numerals based representation, i.e., XCVII -> 24 + 3 + 22 + 9 + 9 = 67. [Gudipati] 97 = reversal(9*7 + 9+7) is the only prime with this property. [Firoozbakht] The continued fraction for π to the fourth power starts with 97. The first four pairs of digits following the decimal point of 1/97 are powers of three: 1/97 = 0.01030927.... [Hill] The first ever NASCAR win for Plymouth and the Chrysler Corporation was powered by a strictly stock flathead engine that produced 97 horsepower. Generally, one jigger (one and a half ounces) of liquor (gin, rum, vodka, and whiskey) contains 97 calories. [Larsen] 97 = π(π(9)^π(9) + π(7)^π(7)). Note that the prime 97 is the only integer with this property. [Firoozbakht] The largest known prime p with the property that when writing down all the natural numbers from 0 to p one uses p odd digits. [Capelle] The word NINETYSEVEN contains smoothly undulating constants and vowels. Is there a larger example? [Johnson] In the middle of 97 insert (97 - 1) and you get 9967, which is also prime. Put (97 - 1) in the middle of 9967 and you get 999667, which is another prime. Put (97 - 1) in the middle again and you get 99996667, yet another prime. After inserting (97 - 1) in the middle once more, it is left for the prime curiologist to find the factors of 9999966667. [Honaker] 97 = 4! * 4 + 4/4. [Dunn] There are 97 non-cubic 3-dimensional crystallographic groups without reflection planes. [Post] Vernon Dalhart's version of the "Wreck of Old 97" is sometimes cited as the American music industry's first million-seller. The number of primes with exactly 3 distinct digits. [Beedassy] 97 and its double (194) and triple (291) use the same number of characters (five) when expressed in Roman numerals: XCVII, CXCIV, and CCXCI. [Meller] The smallest prime that can be expressed as the sum of first odd composite numbers (9 + 15 + 21 + 25 + 27). [Silva] Dudeney numbers are exactly 13, 83, 173, 183, 263, 273. The sum 97 = 1 + 8 + 17 + 18 + 26 + 27 is an emirp. [Poo Sung] The only nonagenarian prime. British logician, mathematician, and philosopher Bertrand Russell lived to be 97. The number of ways to form two fractions that add up to 1 if all distinct digits 0 through 9 are used in each case. There is only one such case that uses the number 97. Can you find it? The sum of all prime factorials less than or equal to 97 is prime after subtracting 1. [Silva] The smallest emirp p such that the reversal of all the five numbers 2^k*p, k < 6 are prime. [Firoozbakht] The smallest prime that has the same (prime) digital root as its subscript: 97 is the 25th prime P25. [Beedassy] All ZIP Codes in the state of Oregon begin with the digits '97'. [Green] The smallest emirp followed by another with the same end digit. [Silva] Largest prime which is less than the sum of square of its digits (i.e., 97 < 9^2+7^2). [Gupta] The emirp number of primes between the emirp pair 107 and 701. This is a first occurrence. [Blankenship] 97272/1087 = 3.141592654.... [Meller] If A=1, B=4, C=1, ... , Z=8, using the decimal digits of π, then 'LUNAR PRIME NUMBER' is a lunar prime number. [Homewood] The smallest prime (emirp) equal to the sum of first n odd composite numbers (n = 5), i.e., 97 = 9 + 15 + 21 + 25 + 27. [Loungrides] The larger of only two double-digit primes that remain prime when inserting one, two, three or four zeros between the digits. The other is 71. Note that both of them are emirps. [Loungrides] The number 9797 cannot be written as the sum of consecutive cubes. [Wesolowski] The smallest prime (the only emirp) that is the sum of the reversals of two consecutive double-digit composite numbers, i.e., (39, 40). [Loungrides] The only prime sum of consecutive prime fourth powers. [Silva] The sum of all emirps under 10^10 has sum of digits equal to the largest prime under 10*10. [Merickel] A forward-K appears struckout, and corrected with a backwards K symbol at position 97 of Z340. Note that a "strikeout looking" in baseball—in which the batter does not swing and the third strike is called by the umpire—is usually denoted by a ꓘ. [Honaker] The smallest prime that is the sum of a prime number of distinct primes with prime subscripts: 97 = 3 + 5 + 17 + 31 + 41 = P2 + P3 + P7 + P11 + P13 [Beedassy] The only double-digit prime p such that 100-p and 100+p are both primes. [Loungrides] Is (97^p+1)/(97+1) composite for all odd primes p? [Honaker] The sum of the six positive integers that are equal to the sum of digits of their cubes. [Gaydos] Mathematician, concert pianist, logician, Taoist philosopher, and magician Raymond Smullyan turned 97 on May 25, 2016. A circle 97 millimeters in diameter is very close to 1 foot in circumference. [Gaydos] The smallest number n, (it is also prime and emirp), such that the product of first n positive even numbers minus 1 is a prime greater than a googol. Note that the product of first n even numbers minus 1 is given by the form 2^n*n!-1, where n is the number of even numbers. May we call the primes of this form, “almost evenian primes”? [Loungrides] Visitors may climb 97 steps to the lookout platform at The Homesteads Tower near Crossville, Tennessee. 97 is the largest prime mentioned in the Prime Numbers Rap Song by Kevin Barnhart. The population standard deviation of the first 97 natural numbers is "perfect." [Honaker] (97, 101, 103) is the larger of the only two known cases of successive primes p < q < r such that p|(2q*2r + 1), i.e., 97 divides ((2*101)*(2*103) + 1). The smaller such case is (3, 5, 7). [Jha] The smallest prime that is the arithmetic mean of the first n invertible primes: ((19+61+109+199)/4). [Jha] The setting is 97 years after a devastating nuclear apocalypse wipes out almost all life on Earth. "The 100" are a subgroup of the Sky People and the namesake of the TV series. They are one hundred juvenile delinquents sent to what was formerly Virginia to determine if the planet had become habitable. Consider yourself a prime curiologist if you recognized that 97 is the largest prime number less than 100. "Process 97" was the fictional secret formula in the film "The House On 92nd Street" (1945). The last two-digit number to appear in the digits of a square, first appearing in 176^2 = 30976. [Gaydos] None of the 97 consecutive integers from 2655397632 to 2655397728 are semiprimes. [Gaydos] The Kryptos Sculpture was unveiled on the grounds of the CIA complex in Langley, Virginia. It was built by American artist Jim Stanborn and contains four encrypted messages. Three of the messages have been solved but the fourth, which is 97 letters long, is still waiting to be deciphered. [Homewood] The largest two-digit prime multiplied by its two digits gives a near-repunit number. [Leonardis] The smallest prime that is the sum of three distinct Fibonacci primes, i.e., 97 = 3 + 5 + 89. [Honaker] 2! + 3! + 5! + 7! + 11! + ... + 97! - 1 is prime. [Xavier] Howard "Ki" Punches had a passion for prime numbers. He left us 97 curios. A prime greater than 97 has never been found of form 2^n+3^n. [Elemer] The concatenation of the first 97 positive integers is a semiprime. [Resta] [Roman numeral C] - [English alphabet code C] = 97. [Worrom] Duplodnaviria is a realm of viruses that includes all double-stranded DNA viruses that encode the HK97 fold major capsid protein. [Dolja]

(There are 10 curios for this number that have not yet been approved by an editor.)