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  2. Goldbach's conjecture - Wikipedia

    en.wikipedia.org/wiki/Goldbach's_conjecture

    In 1930, Lev Schnirelmann proved that any natural number greater than 1 can be written as the sum of not more than C prime numbers, where C is an effectively computable constant; see Schnirelmann density. [13] [14] Schnirelmann's constant is the lowest number C with this property. Schnirelmann himself obtained C < 800 000.

  3. List of prime numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_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.

  4. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Positive numbers: Real numbers that are greater than zero. Negative numbers: Real numbers that are less than zero. Because zero itself has no sign, neither the positive numbers nor the negative numbers include zero. When zero is a possibility, the following terms are often used: Non-negative numbers: Real numbers that are greater than or equal ...

  5. Prime number - Wikipedia

    en.wikipedia.org/wiki/Prime_number

    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 ...

  6. Largest known prime number - Wikipedia

    en.wikipedia.org/wiki/Largest_known_prime_number

    [1] [2] A plot of the number of digits in the largest known prime by year, since the electronic computer. The vertical scale is logarithmic. A prime number is a natural number greater than 1 with no divisors other than 1 and itself. According to Euclid's theorem there are infinitely many prime numbers, so there is no largest prime.

  7. Goldbach's weak conjecture - Wikipedia

    en.wikipedia.org/wiki/Goldbach's_weak_conjecture

    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). In 2013, Harald Helfgott released a proof of Goldbach's weak conjecture. [2]

  8. Fundamental theorem of arithmetic - Wikipedia

    en.wikipedia.org/wiki/Fundamental_theorem_of...

    Then, by strong induction, assume this is true for all numbers greater than 1 and less than n. If n is prime, there is nothing more to prove. Otherwise, there are integers a and b, where n = a b, and 1 < a ≤ b < n. By the induction hypothesis, a = p 1 p 2 ⋅⋅⋅ p j and b = q 1 q 2 ⋅⋅⋅ q k are products of primes.

  9. Greater-than sign - Wikipedia

    en.wikipedia.org/wiki/Greater-than_sign

    In mathematical writing, the greater-than sign is typically placed between two values being compared and signifies that the first number is greater than the second number. Examples of typical usage include 1.5 > 1 and 1 > −2. The less-than sign and greater-than sign always "point" to the smaller number.