> thanks,i 'll look it up.
> already made some mistakes,161 and surely 875 aren't p after all, but
> interestingly they're at position 12 AND 24..
>
(the whole thing about digit reversal in prime numbers is fascinating,
as is your note, what i can understand of it.)
btw: have you ever seen some kind of spatial diagram of primes.
not exactly sure what i saw, but i think it involved primes,
it was beautiful, a kind of mandala or radial snowflake pattern.
haven't been able to locate this in my papers. I used to dig alot
of damaged mathematics books out of the trash when i worked at the
half-priced books warehouse. I got my two-volume mathematics
encyclopedia that way. Lovely things going into the trash for a few
little dings.
I like the 'Primes Curiosity' pages.
here is the entry for '23':
The smallest prime whose reversal is a power: 32 = 25. [Trigg]
23 is the smallest prime for which the sum of the squares of its
digits is also an odd prime. [Trotter]
The floor function of e^ = 23.
23 is formed from the concatenation of the first two primes.
The number of elementary 2-fold polychords. [Keith]
The smallest prime number which is not the sum of two Ulam numbers.
[Guy]
230 + 231 + 232 + 233 + 235 = 6449063 and the sum of 6 + 4 + 4 + 9 + 0
+ 6 + 3 can be written as 3 x 2 + 2 x 2 + 2 x 2 + 3 x 3 + 0 + 3 x 2 +
3 = 32, the reversal of 23. [Gevisier]
23 is the only prime number p such that p! is p digits long. [Gupta]
The smallest isolated prime, i.e., not an element of a set of twin
primes. [Francis]
23 requires 9 positive cubes to represent it. Note that (23) = 9.
[Honaker]
The top speed of an American crow is 23 miles per hour. [Stidham]
Hilbert's problems are a list of 23 problems in mathematics put forth
by David Hilbert in the year nineteen hundred. The problems were all
unsolved at the time.
Psi (y) is the 23rd letter of the Greek alphabet. [Roberts]
2n is congruent to 3(mod n) for n = 4700063497, but for no smaller n >
1. [Lehmer]
Homo sapiens have 23 pair of chromosomes.
(35 + 53)/(3+5 + 5+3) = 23. [Kulsha]
The largest prime with its least quadratic non-residue greater than
sqrt(p). [Nagell]
23 is the largest integer that is not the sum of distinct powers.
[Wells]
Cyclotomic rings are formed by adjoining the n roots of unity to the
integers. Montgomery and Uchida independently showed that the first of
these rings to have class number greater than one is formed by
adjoining the 23rd roots of unity. [Bonan]
There are only 23 odd abundant numbers below 104.
23 is the smallest prime of the form 10*p + 3 that is not the sum of
two squares, where p is prime. [Murton]
11111111111111111111111 (23 ones) is a Repunit prime.
11111 x 111111 + 11111111111 + 1 (23 ones) is prime. [Fougeron]
2n + 3n is prime for n = 0, 1 and 2. [Trotter]
Sherlock Holmes and Doctor Watson lived at 221b Baker Street for a
period of 23 years. [Haga]
There are 23 disks in the human spine. [McCranie]
23! is the least factorial in which the digits 0 through 9 appear at
least once. [Das]
23 = 14 + 23 + 32 + 41 + 50. [Trotter]
23 is the only prime of the form p*q + p + q and p*q - p - q, where p
and q are two successive primes (3*5 + 3 + 5 = 5*7 - 5 - 7 = 23.
[Teofilatto]
There are 23 definitions in Book I of Euclid's Elements.
23 was Michael Jordan's jersey number.
(23) = 32. [Caldwell]
23 = 5 + 7 + 11. Do you see the first five consecutive primes? [La
Haye]
23 is the smallest prime number with consecutive digits. [Capelle]
There are 23 counties in Maryland. [Litman]
23 = 3 times the third prime + twice the second prime + once the first
prime. [Murthy]
2! + 3! = 23. [Murthy]
23 = - (22 - 33). [Murthy]
The smallest prime which differs from its successor by 6. [Murthy]
Thrice three and twenty for pleasure true and plenty. [Croll]
The smallest prime of form pp - qq, where p and q are primes. [Murthy]
Smallest prime p such that 90*p+11, 90*p+13, 90*p+17, 90*p+19 are all
primes. [Russo]
The sum of the forth powers of the first 23 primes is prime.
[Patterson]
The state of Wyoming has 23 counties. [Dobb]
23 is the smallest prime number that is equal to the product plus sum
of Twin primes, i.e., 3*5 + (3+5) = 23. [Wagler]
At the height of his career, Professor John F. Nash, Jr. interrupted a
lecture to announce that a photo of Pope John XXIII on the cover of
Life was actually Nash in disguise and that he knew this because 23
was his favorite prime number. [Hageman]
The smallest multi-digit Tetranacci prime: a(n) = a(n-1) + a(n-2) + a
(n-3) + a(n-4). [Russo]
The smallest prime p that divides the number of digits of p!. [Russo]
The largest integer which cannot be expressed as the sum of two
squareful numbers (numbers divisible by the square of a prime).
[Rupinski]
The sum of the square roots of the first 23 primes is very near the
32nd prime. [Rupinski]
In a room of just 23 people, a greater than 50% chance exists that two
of the people will share a common birthday.
Archbishop Ussher argued that the world was created on Sunday 23
October 4004 B.C. Note that he was Primate of All Ireland. [Delval]
In the Charles Dickens novel "A Tale of Two Cities," each beheading
was counted down. Sidney Carton, the insolent, indifferent, and
alcoholic attorney, was guillotine victim number 23. [Nunes]
The Brazilian football player nicknamed Pelé (considered by many to be
the best player of all time) was born on 23 October 1940.
David Beckham (hailed as one of the best English soccer players of all
times) dons the No. 23 Real Madrid white jersey.
'Twenty-three, skidoo!' is an American catch phrase.
Julius Caesar was stabbed 23 times when he was assassinated.
23 is the second Woodall prime.
'The Immortal Game' of chess played between Anderssen and Kieseritzky
lasted only 23 moves. [Patterson]
23 = 1! + (2! + 2!) + (3! + 3! + 3!). [Capelle]
There are exactly 23 nonisomorphic trees with 2^3 vertices.
[Patterson]
According to biorhythm theory, everyone has a 23-day physical cycle.
[Miller]
One 2 and one 3 (23) divides two 2's and three 3's (22333). [De Geest]
2^23 + 3^23 + 2*3 is prime. [LaurV]
There are 23 primes which can not be written as a sum of (nonunit)
cubes. Note that 23 is the largest prime which cannot be written as a
sum of (nonunit) squares. [Hartley]
There are 23 distinct pairs of primes less than 1000 that sum to 1000.
[Patterson]
The world's fastest human can average 23 miles/hour in the 100 meter
dash. [Adrion]
23 degrees Celsius is "room temperature" on Earth. [Ballinger]
The word hell is found only 23 times in the King James Version of the
New Testament, and most of those are by Jesus. [Van Empe]
The Sundial Bridge, a footbridge over the Sacramento River at Redding,
California, is 23 feet wide. [Haga]
23 is the only prime of the form p*q + p + q and p*q - p - q, where p
and q are Twin primes (3*5 + 3 + 5 and 5*7 - 5 - 7 = 23.) [Teofilatto]
23 is the smaller prime factor of 2^11-1, the smallest composite
Mersenne number with prime exponent. [Terr]
23 is the first Happy number that is not of the form 3n+1. [Axoy]
23 is the only known number p where Rp is a repunit prime, 10^p-p is
prime, and p is a primefactor of a Mersenne number with repunit
exponent. I.e., 23 is factor of 2^(11)-1). [Luhn]
23*3-32*2 = (3+2)*(3-2). [Losnak]
The primes up to 23 and the squares of primes up to 23 separated by
zeroes form primes. [Gallardo]
23 = 2(mod 3) = 3(mod 2). [Losnak]
23 is the smallest and only prime of the form 2x^2 - y^2 and 3x^2 -
y^2, where x and y are two consecutive numbers. [Teofilatto]
23 is the smallest prime equal to the sum of three primes in two ways:
5+7+11 = 3+7+13 = 23. [Teofilatto]
To get the largest 23-digit prime one only needs to subtract 23 from
10^23. [De Geest]
23 = (2^2 + 3^3) - (2! + 3!). [Teofilatto]
William Shakespeare died on his birthday (23 April). [Dowdy]
Episode 18 of the TV series "Lost" revolves around a mysterious
sequence of six numbers. The only prime in the sequence is 23.
[Hartley]
23 is the smallest prime which differs from its reverse by a square.
[Poo Sung]
The smaller prime of the smallest set of two consecutive multidigit
primes, i.e., {23, 29}, whose sum of digits (i.e., 5, 11) is another
set of two distinct primes. [Gupta]
