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The number of pieces that could be seen in a 6 × 6 × 6× 6 Rubik's Tesseract. 1041 = sum of 11 positive 5th powers [36] 1042 = sum of 12 positive 5th powers [37] 1043 = number whose sum of even digits and sum of odd digits are even [38] 1044 = sum of distinct powers of 4 [35] 1045 = octagonal number [39]
The first 1000 prime numbers ... A cluster prime is a prime p such that every even natural number k ≤ p − 3 is the difference of two primes not exceeding p. 3, 5 ...
A number where some but not all prime factors have multiplicity above 1 is neither square-free nor squareful. The Liouville function λ(n) is 1 if Ω(n) is even, and is -1 if Ω(n) is odd. The Möbius function μ(n) is 0 if n is not square-free. Otherwise μ(n) is 1 if Ω(n) is even, and is −1 if Ω(n) is odd.
In 1747, Leonhard Euler completed what is now called the Euclid–Euler theorem, showing that these are the only even perfect numbers. As a result, there is a one-to-one correspondence between Mersenne primes and even perfect numbers, so a list of one can be converted into a list of the other. [1] [5] [6]
Where to invest $1,000 right now? ... After Palantir's latest earnings numbers came out, many analysts upgraded their price targets for the stock. ... it's even more of one now.
While Nicomachus had stated (without proof) that all perfect numbers were of the form () where is prime (though he stated this somewhat differently), Ibn al-Haytham (Alhazen) circa AD 1000 was unwilling to go that far, declaring instead (also without proof) that the formula yielded only every even perfect number. [15]
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