**819**= 3

^{2}x 7 x 13.

**819**is 1100110011 in base 2 (binary) and 333 in base 16.

**819**is the largest three-digit number whose square (670761) and cube (549353259) use different digits.

**819**is the smallest number such that it and its successor (820) are both the product of two primes and the square of a prime: 820 = 2

^{2}x 5 x 41.

*819*-

*line television*standard.

Source: Number Gossip

## 1 comment:

Other properties of the number 819

The number 819 can be represented as:

819=11^2+13^2+23^2=13^2+17^2+19^2

819=2^3+5^3+7^3+7^3=3^3+4^3+6^3+8^3

819=3^6+90

819 divides 64^2-1

819 is the sum of consecutive prime numbers from 13-79:

819=Sum[P,P,13,79]=13+17+19+23+...+71+73+79

819 is the sum of the squares between 1^2 and 13^2:

819=Sum[n^2,1,13]=1^2+2^2+3^2 +...+ 11^2+12^2+13^2,see A000330

819=n(n+1)(2n+1)/6 with n=13 is the square pyramidal number indicated

As a difference of two squares:

819=50^2-41^262^2-55^2

As opposed to a square and another number with different exponents:

819 = 30 ^ 2-3 ^ 4 = 38 ^ 2-5 ^ 4

As Pythagorean triples:

819^2=315^2+756^2

819^2+1900^2=2069^2

819^2+6820^2=6869^2

819^2+4100^2=4181^2

It can also be represented as the sum of a square and a cousin

819=10^2+719=20^2+419=16^2+563

Rafael Parra Machio

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