• Sorting the digits of 2¹⁰⁰⁵ in ascending order we obtain a prime of 273 digits.

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1005 has 8 divisors (see below), whose sum is σ = 1632. Its totient is φ = 528.

The previous prime is 997. The next prime is 1009. The reversal of 1005 is 5001.

It is a sphenic number, since it is the product of 3 distinct primes.

It is not a de Polignac number, because 1005 - 2³ = 997 is a prime.

It is a Curzon number.

It is a plaindrome in base 9.

It is a junction number, because it is equal to n+sod(n) for n = 984 and 1002.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1009) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 19 + ... + 48.

It is an arithmetic number, because the mean of its divisors is an integer number (204).

1005 is a gapful number since it is divisible by the number (15) formed by its first and last digit.

It is an amenable number.

1005 is a deficient number, since it is larger than the sum of its proper divisors (627).

1005 is an equidigital number, since it uses as much as digits as its factorization.

1005 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 75.

The product of its (nonzero) digits is 5, while the sum is 6.

The square root of 1005 is about 31.7017349683. The cubic root of 1005 is about 10.0166389658.

Adding to 1005 its reverse (5001), we get a palindrome (6006).

It can be divided in two parts, 100 and 5, that added together give a triangular number (105 = T₁₄).

The spelling of 1005 in words is "one thousand, five".