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Super Simple Songs was started in 2004 by teachers of a small English school in Japan. They created their own songs in place of children's songs that were too complex and difficult to be used in teaching. After increasing in popularity from other teachers, they released their first CD. At some point, Super Simple Songs began uploading videos to ...
This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes.
Ulam spiral of size 201×201. Black dots represent prime numbers. Diagonal, vertical, and horizontal lines with a high density of prime numbers are clearly visible. For comparison, a spiral with random odd numbers colored black (at the same density of primes in a 200x200 spiral). The Ulam spiral or prime spiral is a graphical depiction of the ...
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...
The Music of the Primes (British subtitle: Why an Unsolved Problem in Mathematics Matters; American subtitle: Searching to Solve the Greatest Mystery in Mathematics) is a 2003 book by Marcus du Sautoy, a professor in mathematics at the University of Oxford, on the history of prime number theory. In particular he examines the Riemann hypothesis ...
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Rowland (2008) proved that this sequence contains only ones and prime numbers. However, it does not contain all the prime numbers, since the terms gcd(n + 1, a n) are always odd and so never equal to 2. 587 is the smallest prime (other than 2) not appearing in the first 10,000 outcomes that are different from 1. Nevertheless, in the same paper ...
Thus, all Mersenne numbers M4k +1 are congruent to 11 modulo 20 and end in 11, 31, 51, 71 or 91, while Mersenne numbers M4k −1 ≡ 7 (mod 20) and end in 07, 27, 47, 67, or 87. For the perfect numbers, define Pn = 2n−1Mn be the value which is perfect if Mn is prime. When n = 4k +1 and k > 0, 24k ≡ 16 (mod 20), so Pn ≡ 16×11 ≡ 16 (mod ...