97
(another Prime Pages' Curiosity)
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Carla Kik © 2004
There exists a positive integer n such that the number of primes in the interval [97, 97 + n] equals pi(n). Here n = 16. No other odd prime besides 97 is known to have this property.

The largest two-digit prime.

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 non-titanic 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 continued fraction for pi 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]

The largest two-digit prime whose cube is zeroless. [Pattterson]

97 = pi(pi(9)^pi(9) + pi(7)^pi(7)). Note that the prime 97 is the only integer with this property. [Firoozbakht]

97 is a 4-dimensional Centered Cube prime. Note that 97 = 2^4 + (2+1)^4. [Post]

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]




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