509841952128000 has 880 divisors, whose sum is σ = 1904240094460704. Its totient is φ = 135659092377600.

The previous prime is 509841952127983. The next prime is 509841952128043. The reversal of 509841952128000 is 821259148905.

509841952128000 is a `hidden beast` number, since 5 + 0 + 9 + 8 + 419 + 5 + 212 + 8 + 0 + 0 + 0 = 666.

It is a super-2 number, since 2×509841952128000² (a number of 30 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 4738122199 + ... + 4738229801.

Almost surely, 2^{509841952128000} is an apocalyptic number.

509841952128000 is a gapful number since it is divisible by the number (50) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 509841952128000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (952120047230352).

509841952128000 is an abundant number, since it is smaller than the sum of its proper divisors (1394398142332704).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

509841952128000 is a wasteful number, since it uses less digits than its factorization.

509841952128000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 108107 (or 108070 counting only the distinct ones).

The product of its (nonzero) digits is 2073600, while the sum is 54.

The spelling of 509841952128000 in words is "five hundred nine trillion, eight hundred forty-one billion, nine hundred fifty-two million, one hundred twenty-eight thousand".