What number is 744?

744 is the nineteenth number of the form where , and represent distinct prime numbers ( 2, 3, and 31; respectively). It can be represented as the sum of nonconsecutive factorials , as the sum of four consecutive primes , and as the product of sums of divisors of consecutive integers ; respectively:

What is the Euler totative value of 744?

744 is equal to the sum between the 41st and 44th indexed prime numbers, inclusive. Indices 15 and 16 of σ ( n) multiply to 240, which is the Euler totient value of 744, and add to 31 which is the largest prime that is not a totative of 744 (less than).

How many prime numbers are there between 71 XXIX and 744?

Taking the sum of the three terms that lie between 71 [xxix] and 744 (i.e. 130, 235, 420) yields 785 = 28 2 + 1, whose aliquot sum is 163, [xxx] the thirty-eighth prime number.