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Can odd perfect numbers exist after 100000000000000000000000000000000000000000000000000?
So far, no odd perfect numbers have been found to exist. If and only if one does exist, it will be far larger than the number in the question. In fact, it has been proven concretely that if an odd perfect number exists, it is greater than 10^300, and it is conjectured that if such a number exists, it is greater than 10^500.
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Is 495 a perfect number?
No, it isn't. In fact, it is not known whether are odd perfect numbers exist. The first perfect numbers are 6, 28, 496, and 8128.
Are there more mersenne primes known as there are perfect numbers?
There is a one-to-one relationship between even perfect numbers and Mersenne primes. It is unknown whether there are any odd perfect numbers.
Are there an infinite number of perfect numbers why is that so?
It is not yet known:Whether there is an infinite number of even perfect numbersWhether there is any odd perfect number
Is 7 the only perfect number on the form xn yn?
No. Because 7 is not even a perfect number; it is conjectured (not proven) that there are no odd perfect numbers only even ones and 7 is an odd number - it has been proven that if there is an odd perfect number it has to be extremely large, much-much-much larger than 7)
What even number less than 100 has an odd number of factors?
Perfect squares have odd numbers of factors. The perfect squares less than 100 are: 1,4,9,16,25,36,49,64,81,100. 64 seems to fit both criteria.
