Sunday, 12 February 2012

Today is 43 day of the year.
43 is prime.
43 is the smallest prime number that is not a Chen prime.
43 is a Wagstaff prime.
43 is the largest McNugget number.
43 is a member of the primitive, Pythagorean triple (43, 925, 925).
43 is a toothpick number, nicely illustrated here.
43 is a lucky number.
43 is a member of a sexy pair of primes and a sexy triplet of primes.
43 is the largest number that cannot be made up from positive multiples of 5 and 12.

Saturday, 11 February 2012

Today is 42 day of the year.
42 = 2 x 3 x 7.
42 = 6 x 7, it is a pronic, oblong, rectangular or heteromecic number.  This is the best excuse I can think of to consume an oblong biscuit that has been dunked in a nice cup of tea.
42 is a sphenic number, thus it has exactly eight divisors.
42 is a self number.
42 = 19 + 23, the sum of two consecutive primes.
42 is the sixth cake number.
42 is a Catalan number, which means that, amongst other things, it is the number of ways:

• that a seven sided polygon can be cut into five triangles;
• that parentheses can be placed in a sequence of six numbers to be multiplied, two at a time;
• that paths of length 10 can pass through a 5-by-5 grid while not rising above the main diagonal.

42 is the number of minutes it would take to fall through a hole bored through the planet Earth.
42 is, of course, The Answer To The Ultimate Question Of Life, The Universe, And Everything.

Friday, 10 February 2012

Today is 41 day of the year.
41 is prime.
41 is a Newman-Shanks-Williams prime.
41 is a Proth prime.
41 is a Sophie Germain prime.
41, 83, 167 is a Cunningham chain and the smallest chain of three primes.
41 = 2 + 3 + 5 + 7 + 11 + 13, the sum of the first six primes.
41 = 11 + 13 + 17, the sum of three consecutive primes.
41 is the second smallest integer that can be expressed as the sum of consecutive primes.
41 is a member of two primitive, Pythagorean triples (9, 40, 41) and (41, 840, 841).

Thursday, 9 February 2012

Today is 40 day of the year.
40 = 2^3 x 5
40 is an octagonal number.
40 is a pentagonal pyramidal number.
Forty is the only number whose word contains letters in alphabetical order.

Wednesday, 8 February 2012

Today is 39 day of the year.
39 = 3 x 13.
39 = 3 + 5 + 7 + 11 + 13, the sum of five consecutive primes, the sum of all the primes between the two factors.
39 is a member of two primitive, Pythagorean triples (39, 80, 89) and (39, 760, 761).
39 is member of the sequence that remains after applying Flavius Josephus' sieve.
39 is the smallest number to have a multiplicative persistence of three.
3 x 9 = 27
2 x 7 = 14
1 x 4 =   4
39 is a member of the delightfully self-referential Aronson's sequence.
39 is a member of the delightfully silly Iccanobif numbers.

Tuesday, 7 February 2012

Today is 38 day of the year.
38 = 2 x 19
38 = 2^2 + 3^2 + 5^2, the sum of the first three primes squared.
38 is the largest even number that cannot be written as the sum of two odd composite numbers which are {9, 15, 21, 25, 27, 33, 35).
38 is not a member of any primitive, Pythagorean triple anywhere in the universe.

Monday, 6 February 2012

Today is 37 day of the year.
37 is prime.
37 is the maximum number of pieces of pizza one can create from 8 cuts, 37 is a lazy caterer number.
37 is an emirp.
37 is a lucky number.
37 is a member of two primitive, Pythagorean triples (12, 35, 37) and (37, 684, 685).
37 is the fortieth and forty third members of Alcuin's sequence.

Sunday, 5 February 2012

Today is 36 day of the year.
36 = 2^2 x 3^2, thus 36 is a powerful number.
36 = 17 + 19 = 5 + 7 + 11 + 13, 36 can be expressed as the sum of consecutive primes in two ways.
36 is the smallest number that can be expressed as the sum of consecutive primes in more than one way.
36 is a square number.
36 is a triangular number.
36 is the only triangular number whose square root is a triangular number, proof anyone?
36 = 1^3 + 2^3 + 3^3 (Sloane's A000537)
36 is a member of two primitive, Pythagorean triples (36, 77, 85) and (36, 323, 325)
There are 36 different tilings of a four by four chess board with dominoes.
36 is the smallest number with exactly 9 divisors; 1, 2, 3, 4, 6, 9, 12, 18, 36.

Saturday, 4 February 2012

Today is 35 day of the year.
35 = 5 x 7, 35 is a semiprime, in particular the product of twin primes.
35 = 2^3 + 3^3, the sum of the cubes of two consecutive primes.
35 is a tetrahedral number or, equivalently, the sum of the first five triangular numbers.

35 is a member of two primitive, Pythagorean triples (12, 35, 37) and (35, 612, 613).

35 is a member of Omar Pol's toothpick sequence.
35 is a brilliant number.
35 is a binary digitally balanced number.

Friday, 3 February 2012

Today is 34 day of the year.
34 = 2 x 17
34 is a member of the Fibonacci sequence.
34 = 3^2 + 5^2, the sum of the squares of two consecutive primes.
Since 5^2 = 3^2 + 4^2 then
34 = 3^2 + 3^2 + 4^2

Thursday, 2 February 2012

Today is 33 day of the year.
33 = 3 x 11
33 is a member of two primitive, Pythagorean triples (33, 56, 65) and (33, 544, 545).
33 is a lucky number.

Wednesday, 1 February 2012

Today is 32 day if the year.
32 = 2^5
32 is a happy number.
32 is the member of one primitive, Pythagorean triple (32, 255, 257).
32 is a Leyland Number because 2^4 + 4^2 = 32
32 = 1^1 + 2^2 + 3^3