# 67

This number is a prime.

John Pilkins ©2003 |

^{67}- 1 was prime, but it's composite.

The smallest two-digit Hyper-Cullen 2nd species prime, i.e., a prime of the
form *n* * 2^{n} + (*n* - 1). [Russo]

The largest prime which is not the sum of distinct squares. [Crespi de Valldaura]

π(6*7) = 6+7. [Firoozbakht]

67 = sqrt(9!/(9 * 9) + 9). [Poo Sung]

5^{67} starts with the digits 67. [Hartley]

The hull number of the U.S. Navy's aircraft carrier USS *John F. Kennedy* (CV-67).

The smallest prime which contains all ten digits when raised to the tenth power. [Patterson]

The "Summer of Love" was a phrase given to the summer of '67, describing (personifying) the feeling of being in San Francisco that summer when the hippie movement came to full fruition.

If A = 1, B = 6, C = 1, D = 8, ... , (using the digits of the Golden Ratio), then 'MARIN MERSENNE' = 67; a prime exponent that he himself believed would produce a Mersenne prime number, but which later was proved to be composite [Homewood]

The inventor of natural logarithms (John Napier) died at the age of 67.

*67 ("star 67") is a free phone feature that blocks sending name and phone number on an outgoing individual call. Use *67 + number being dialed (must be done for each call). [Greer]

The smallest prime *p* that divides the number of composites less than the (*p* + 1)th prime. [Honaker]

Using the alphabet code, the value of 67 in its Roman numeral-based representation (LXVII) is the reversal of 67. [Necula]

In the opening scenes of the movie *Hard Target*, set in New Orleans, a horse and carriage numbered 67 rumbles by. [Haga]

The Escher compound that appears in the "Waterfall" lithograph by M. C. Escher divides the three component cubes into 67 individual cells. [Post]

6^{7} is the sum of a twin prime pair. [Rivera]

Longitude 67 degrees West passes through the easternmost city in the United States (Eastport, Maine). A prime place to see the sunrise. [Punches]

2^6 + 2^1 + 2^0 = 26 + 21 + 20 = 67. [Morse]

Charles Lindbergh was the 67th man to make a non-stop flight over the Atlantic Ocean. (The first were Alcock and Brown, the 31 men on the English dirigible R34, and the 33 men on Zeppelin-Airship LZ126.) [Caldwell]

A new born infant is considered full-term when the gestation age in weeks lies between *p*_{k+6} and *p*_{k+7}, where *p*_{k} = 6+7 and *p*_{n} is the nth prime (i.e., between 37 and 41 weeks). [Beedassy]

The sum of all idoneal primes. (A positive integer *m* is idoneal if and only if it cannot be written as *ab* + *bc* + *ac* for integer *a*, *b*, and *c* with 0 < *a* < *b* < *c*.) [Loungrides]

Fresh milk has a pH of 6.7 and is therefore slightly acidic. [O'Mahony]

The largest known prime number p for which the decimal
expansion of 2^{p} does not
contain any pair of consecutive equal digits. It's also the
case for the decimal expansion of
3^{p}. [Capelle]

The largest known prime number p for which the decimal
expansion of 2^{p} does not
contain any zero. [Capelle]

Smallest multidigit prime whose square (i.e., 4489) and cube (i.e., 300763) consist of different digits. [Gupta]

Smallest odd prime number of bicentered 3-valent (or boron, or binary) trees with n nodes. Here with n = 12. [Post]

Any digit n, 1 through 9, times 67 yields a 3-digit number (for the purpose of this discussion make 1*67 = 067), then the concatenation of the first and last digits of the product equals n times 7. E.g., 8*67 = 536 and 8*7 = 56. [Green]

"And that which the rest of the people gave was twenty
thousand drams of gold, and two thousand pound of silver,
and **threescore and seven** priests' garments." (*Nehemiah* 7:72, KJV)

To "be at sixes and sevens" is an informal expression meaning to be thoroughly confused. [Jose]

Foucault's most famous pendulum contained a 67-meter long wire.

One smoot is equal to 67 inches.

The only double-digit prime ab such that p^b+[R(p)]^a is prime, where R(p) is the reversal of p, i.e., 67^7+76^6 = 6253411533899. [Loungrides]

The first prime midway between a square and a cube, (3^2 and 5^3). [Loungrides]

Season 8, Episode 184 of "Dr. Oz" featured a woman who claims to have 67 different personalities. [Stath]

The smallest polite prime that is a concatenation of two successive polite numbers, i.e., (6=1+2+3, 7=3+4). [Loungrides]

The last combat use of the Norden bombsight was in the US Navy's VO-67 squadron.

The smaller of only two non-titanic primes of form n^(n-1)+(n-1) for n a composite number, (case n=4), i.e., 4^3+3. The other prime is for n=10. [Loungrides]

There are 67 four-digit Lynch-Bell numbers. [Shepherd]

Nisan is considered the first month of the Jewish calendar, although it occurs 6 or 7 months after the start of the calendar year. [Tøndering]

The smallest positive integer whose double (134) contains a 3 and whose triple (201) contains a 2. [Gaydos]

Can you solve this week's puzzle (#67) *My Prime* ?