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The strong Goldbach conjecture is in fact very similar to the twin prime conjecture, and the two conjectures are believed to be of roughly comparable difficulty. Goldbach's comet; red, blue and green points correspond respectively the values 0, 1 and 2 modulo 3 of the number.
This conjecture is called "weak" because if Goldbach's strong conjecture (concerning sums of two primes) is proven, then this would also be true. For if every even number greater than 4 is the sum of two odd primes, adding 3 to each even number greater than 4 will produce the odd numbers greater than 7 (and 7 itself is equal to 2+2+3).
A powerful number is a positive integer m such that for every prime number p dividing m, p 2 also divides m. Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form m = a 2 b 3, where a and b are positive integers. Powerful numbers are also known as squareful, square-full, or 2-full.
A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758: Extravagant numbers: 4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, ... A number that has fewer digits than the number of digits in its prime factorization (including ...
3 + 2. Note that the ancient Sanskrit sages discovered many years before Fibonacci that the number of compositions of any natural number n as the sum of 1's and 2's is the nth Fibonacci number! Note that these are not general compositions as defined above because the numbers are restricted to 1's and 2's only. 1=1 (1) 2=1+1=2 (2) 3=1+1+1=1+2=2 ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
And the numbers speak for themselves: Nvidia: if you invested $1,000 when we doubled down in 2009, you’d have $356,514 !* Apple: if you invested $1,000 when we doubled down in 2008, you’d have ...
The smallest such number is 25326001. This means that, if n is less than 25326001 and n is a strong probable prime to bases 2, 3, and 5, then n is prime. Carrying this further, 3825123056546413051 is the smallest number that is a strong pseudoprime to the 9 bases 2, 3, 5, 7, 11, 13, 17, 19, and 23.