Factors of 1729 Day
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Saturday, July 13, 2019
On Saturday, the numbers in the date are the prime factorization of 1,729, a number famous for being the Hardy–Ramanujan number, due to it being the smallest positive integer that can be written as the sum of two positive cubes in two distinct ways. after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital.
I remember once going to see him when he was ill at Putney. I had ridden in taxi cab No. 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
The two different ways are:
- 1729 = 13 + 123 = 93 + 103
1 + 1728 = 729 + 1000 = 1729
It is the third Carmichael number, the first two being 561 and 1105. A Carmichael number is a composite number that is a Fermat pseudoprime to all coprime bases. All Carmichael numbers are pseudoprimes to base two; the smallest Carmichael number that is a strong pseudoprime to binary is 15,841, which is factored as 15,841 = 7 × 31 × 73. The number 1,729 is factored as 1,729 = 7 × 13 × 19, which are the same as the numbers in today’s digital notation (7/13/19 or 13/07/19 depending on the format). Regardless of the format, today is the prime factorization of 1,729 because integer multiplication is commutative and not order-sensitive; you can multiply numbers in any order you wish and still get the same answer. For instance, 3 × 4 = 12 and 4 × 3 = 12.
Sources[edit]
- "[ ]" — e.g. December 31, 1999
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