"961 squared = 31"

Oops, that's supposed to read: the square root of 961 = 31.

Time to catch some sleep.

This post was deleted by dimi3

-2nd try-



Tribe~friend Karina posted the following on January 13th, at 12:12 PM 2006
people.tribe.net/karina/bl...5fea043aa0

It's a nice rundown on the most peculiar prime of all: 13



From the list posted below, the following four were some of the most astounding ones I found personally, further establishing 13 as a most peculiar unity principle:


13 is the concatenation of first two Triangular numbers. [Gupta]

The sum of first 13 prime numbers is 238 (whose sum of digits is 13). [Gupta]

The sum of primes up to and including 13 is equal to the 13th prime. [Gupta]

The sum of the remainders when 13 is divided by all the primes up to 13 is 13. [Murthy]



And these two here were quite 'interesting' I thought:


The U.S. House has voted a total of 13 articles of impeachment against U.S. Presidents: 11 against Andrew Johnson and 2 against Bill Clinton. 13, 11, and 2 are all prime. [Wolfe]

Apollo Lunar Mission number 13, which was aborted while enroute to the moon because of an explosion of a fuel cell in the service module, left the launch pad at 13:13 (CST) hours military time and the accident occurred on April 13. [Cooley]




source:
primes.utm.edu/curios/page.php/13.html







> original forum text copy
(notice the sum of numbers in the posting date... woowoowoo!)



Fri, January 13, 2006 - 12:12 PM


13

"...

The Triskaidekaphobic prime sequence begins: 2, 3, 5, 7, 11, 17, 19, ...

213 - 1 is a Mersenne prime.

There are 13 Archimedean solids.

The smallest emirp (a different prime when reversed).

132 = 169 and (reversing all digits) 312 = 961.

13 is the largest prime that can divide two successive integers of the form n2 + 3. [Monzingo]

1313 - 13 + 1 is prime. [Luhn]

A "baker's dozen" is a group of 13. Its origin can be traced to a former custom of bakers to add an extra roll as a safeguard against the possibility of twelve weighing light.

The first prime gap of 13 occurs between 113 and 127.

There are 13 tricks in each hand of bridge. [Goren]

132 divides 12! + 1.

13 is also a prime Happy number: 13 = 12 + 32 = 10 and 12 + 02 = 1.

The smallest Inconsummate number in base 2. [Conway]

The Number of the Beast is first mentioned in Chapter 13 of the Book of Revelations.

13 is half of -13 + 33. [Stark]

The olive branch on the back of a U.S. dollar bill has 13 leaves. [Weirich]

132 divides (13 - 1)! + 1, thus a Wilson prime.

The Chinese abacus consists of 13 columns of beads.

The smallest permutable prime.

60n2 + 30n - 30 lies between a Twin prime pair for n = 1 to 13. [Blanchette]

Eight additional primes can be produced by altering one digit {11, 17, 19, 23, 43, 53, 73, 83}.

The United States flag once had 13 stars and 13 strips which represented the 13 original colonies.

The smallest prime whose digits are reversed in base 4. [Haga]

There is no elliptic curve over the rationals Q having a rational point of order 13. [Mazur & Tate]

132 = 7 + ... + 19. [Bertuello]

According to a conjecture by Issai Schur, it's the only prime with more than sqrt(p) consecutive quadratic non-residues. Hudson proved this for p greater than 2232.

132 can be expressed as the sum of 1, 2, 3, 4, 5, 6 distinct squares. [Crespi de Valldaura]

The longest recorded flight of a chicken is 13 seconds.

131211109876543212345678910111213 is prime. [Kulsha]

132 turned upside down is prime. [Honaker]

ELEVEN + TWO = TWELVE + ONE is an anagrammatical equation involving 13.

13 is the smallest prime which is the sum of two distinct prime squares (22 + 32). [Gevisier]

Euclid and Diophantus each composed 13 books.

In May, 2001, Ford announced that it would replace 13 million tires on its Ford Explorer SUVs. [Caldwell]

Using the first three primes we have: 23 + 5 = 13. [Trotter]

Alfred Hitchcock's directorial debut was on the film Number 13, which was never completed. [Liebert]

The term paraskevidekatriaphobia was coined by Dr. Donald Dossey and refers to the fear of Friday the 13th. [Hammond]

Osama bin Laden is written with 13 letters. [Gevisier]

A Turing Machine with four conditions can write a maximum of 13 characters. [Luhn]

The Beatles recorded 13 albums during the time in which they were together as a group. [Litman]

One of the most commonly held superstitions in our society is that 13 is unlucky.

The sum of primes up to and including 13 is equal to the 13th prime. [Gupta]

A 13-volume treatise, Almagest, was Ptolemy's greatest work. It provides a mathematical theory of the motions of the Sun, Moon, and planets. [Seymour]

The sum of the remainders when 13 is divided by all the primes up to 13 is 13. [Murthy]

The smallest prime whose sum of digits is a square. [Gupta]

The Mothman of Point Pleasant disappeared exactly 13 months to the day of its arrival (15 Dec 1966 - 15 Nov 1967). [Sturgill]

13 divides the Munster's address (1313 Mockingbird Lane).

Euler had 13 children, only 5 of whom reached adolescence and 3 of whom survived him. [Poo Sung]

The smallest prime of the form p^2+4, where p is prime. [Russo]

The smallest multi-digit prime p such that the sum of all primes less than or equal to p is prime. [Russo]

The sum of the fourth powers of the first 13 primes plus one is prime (6870733). [Patterson]

The smallest Sextan prime: p = (x^6 + y^6 )/(x^2 + y^2 ). [Russo]

If a prime number has the characteristic of (p-1)! = -1 mod p^2, it is a Wilson prime. Only three Wilson primes are known: 5, 13, and 563. [Dobb]

The smallest multi-digit Inert prime: primes congruent to {2, 3} mod 5. [Russo]

(13+1)13 - 13 is prime. [Poo Sung]

The smallest prime that isn't the sum of distinct primes of the form 4n+3. [Russo]

The smallest multi-digit prime p such that its square can be partitioned into 2 or more numbers that are also squares. [Russo]

The smallest multi-digit Weak prime: p(n)<(p(n-1)+p(n+1))/2. [Russo]

The Jewish sage Moses Maimonides established 13 principles of the Jewish faith. [Croll]

Ironically, 13 is the fifth Lucky number. [Emmert]

Patau's Syndrome is a rare inherited abnormality of the chromosomes, also known as Trisomy 13. [Smith]

The largest known Fibonacci Prime P such that F(P) is also prime. [Rupinski]

13 is the concatenation of first two Triangular numbers. [Gupta]

10^999 + 13 is the smallest Titanic composite number in which none of the prime factors are known. [Gupta]

The sum of first 13 prime numbers is 238 (whose sum of digits is 13). [Gupta]

Years normally have twelve full moons, but every now and then a year has 13. This "extra" moon is a Blue Moon. [Passi]

13 = 3^0 + 3^1 + 3^2. [Dilip]

The smallest prime which can be represented as sum of two primes (i.e., 2 + 11) as well as sum of two composite numbers (i.e., 9 + 4). [Gupta]

There are exactly 13 regular rank four locally projective abstract polytopes. [Hartley]

Consider the quadratic residues (mod 13). There are a prime number of distinct residues possible, of which only one is itself prime. 13 is also the only prime quadratic residue of the next prime, 17. [Rupinski]

The largest minimal prime in base 3. [Rupinski]

13 is the smallest prime that cannot be a member of a Sophie Germain pair. [King]

13333333333333/13 is prime. The numerator has thirteen 3's following 1. [Poo Sung]

13 = 3 + 7 + 3. Note that 3^7 + (3+7) = 13^3. [Hawkins]

10^13 + 10^11 + 10^7 + 10^5 + 10^3 + 10^2 + 10^0 is prime. Note that this is the largest non-titanic prime of this form. [Patterson]

213 - 13 is prime. [Schlesinger]

13^13 + 13! + 13*13 + 13/13 + 13+13 and 13^13 + 13*13 + 13/13 + 13+13 are two fifteen-digit primes. [Firoozbakht]

Beethoven's Sonata in C min "Pathetique" is Opus 13. [Necula]

The unique prime sum of squares of two consecutive primes (2^2 + 3^2). [Gallardo]

A game of Yahtzee consists of 13 rounds. [Bailey]

Three planes can cut a donut into a maximum of 13 parts. [LaurV]

132 = 83 - 73, i.e., one solution of the diophantine equation z2 = x3 - y3. [Jun Mizuki]

The U.S. House has voted a total of 13 articles of impeachment against U.S. Presidents: 11 against Andrew Johnson and 2 against Bill Clinton. 13, 11, and 2 are all prime. [Wolfe]

(13^13+131313+13+13+13+13+13+13+13)/13 is a prime involving 13 13's. [Patterson]

The Virginia Opossum usually has 13 nipples efficiently arranged in an open circle with one in the center. [McCarthy]

Apollo Lunar Mission number 13, which was aborted while enroute to the moon because of an explosion of a fuel cell in the service module, left the launch pad at 13:13 (CST) hours military time and the accident occurred on April 13. [Cooley]

The first half-period prime, i.e., for which the period = (p-1)/2.

The 13th Mersenne prime is 2521-1 and the 13th Lucas number is 521. [Poo Sung]

(1!+3!) + (1!*3!) = 13. [Earls]

13 and 31 are the only known Mersenne emirps. [Croll]

pi(13) = 1!*3! [Gupta]

The fear of Friday 13th can be traced back to the suppression of the Templars and the confiscation of their property by Philip IV of France on Friday 13th in October 1307. [Bassano]

13 = prime(1+3) + (1+3) + phi(1+3). Note that 13 is the only number with this property. [Firoozbakht]

13 is the smallest prime of the form p^2 + pq + q. [Teofilatto]

13 is the smallest Abelian group and prime equal to the sum of two homogeneous numerical groups and the sum of its simple numerical groups: (2!+3!) + (2+3). [Teofilatto]

(13^(13+1)) reversed is a Brilliant number. [Andrew]

Cardano divided cubic equations into 13 types in his book, Ars Magna. [Poo Sung]

Write thirteen 13's and delete last digit. Wow, you get a prime! [Avrutin]

The smallest number n such that sigma(n) is reversal of prime(n). [Capelle]

..."