 97 (another Prime Pages' Curiosity) Curios: Curios Search:

Participate:  GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits) 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] The continued fraction for 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 = ( (9)^ (9) + (7)^ (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] Every number is the sum of four squares. As a corollary to work by J. H. Conway, 97 is the largest prime p for which the first square can be taken to be any positive square < p. [Post] The number 9797 cannot be written as the sum of consecutive cubes. [Wesolowski] Mathematician, concert pianist, logician, Taoist philosopher, and magician Raymond Smullyan turned 97 on May 25, 2016. 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.

(There are 31 curios for this number that have not yet been approved by an editor.)