# When was the last perfect number discovered?

## When was the last perfect number discovered?

The 39th perfect number wasn’t discovered until December of 2001, while the last perfect number to be found to date was discovered in December of 2005. Two millennia after Euclid, Euler proved that the formula 2n−1(2n − 1) will yield all the even perfect numbers when n is a Mersenne prime.

### What is the biggest perfect number?

The largest perfect number corresponds to the Mersenne prime 26972593 – 1 (a number with over 2 million digits), the perfect number itself has 4197919 digits.

Is 33550336 a perfect number?

A Perfect Number is a natural number such that its value is equal to the sum of its proper divisors. The first seven Perfect Numbers are: 6, 28, 496, 8128, 33550336, 8589869056, 137438691328.

How many perfect numbers exist?

There are around 51 known perfect numbers. There are only 2 perfect numbers from 1 to 100 which are 6 and 28. The latest perfect number was discovered in 2018 which has 49,724,095 digits.

## What makes 28 a perfect number?

A number is perfect if all of its factors, including 1 but excluding itself, perfectly add up to the number you began with. 6, for example, is perfect, because its factors — 3, 2, and 1 — all sum up to 6. 28 is perfect too: 14, 7, 4, 2, and 1 add up to 28. But perfect numbers aren’t common at all.

### Why is 10 the perfect number?

Today the usual definition of a perfect number is in terms of its divisors, but early definitions were in terms of the ‘aliquot parts’ of a number. An aliquot part of a number is a proper quotient of the number. So for example the aliquot parts of 10 are 1, 2 and 5. Then 31 × 16 = 496 which is a perfect number.

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Is 8128 a perfect number?

8128 is the integer following 8127 and preceding 8129. It is most notable for being a perfect number (its divisors 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, and 4064 add up to 8128), and one of the earliest numbers to be recognized as such.

What is meant by twin prime?

Definition of twin primes : a pair of prime numbers (such as 3 and 5 or 11 and 13) differing by two.

## Why is 11 not a prime number?

Is 11 a Prime Number? The number 11 is divisible only by 1 and the number itself. For a number to be classified as a prime number, it should have exactly two factors. Since 11 has exactly two factors, i.e. 1 and 11, it is a prime number.

### Is 130816 a perfect number?

1 In Eric Temple Bell’s fascinating book2, the seven perfect numbers after 6 are listed as follows: 28, 496, 8128, 130816, 2096128, 33550336, 8589869056. Inasmuch as 511 and 2047 are not primes, it follows that 130816 and 2096128 are not perfect numbers, and they should not have been included in Bell’s list.

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What is perfect number in C++?

A perfect number is equal to the sum of its divisors excluding itself. 1. The number to be checked if it is perfect or not is entered.

Is 0 a narcissistic number?

digits are 0, (none), 153, 1634, 54748, 548834, (OEIS A014576). Since the number of digits is not equal to the power to which they are taken for such numbers, they are not narcissistic numbers.