Cicadas spend most of their time hiding, only reappearing to mate every 13 or 17 years. Two primes are considered as sufficiently secure if they are 2,048 bits long, because the product of these two primes would be about 1,234 decimal digits. The security of this type of cryptography relies on the difficulty of factoring large composite numbers, which is the product of two large prime numbers.Ĭonfidence in modern banking and commerce systems hinges on the assumption that large composite numbers cannot be factored in a short amount of time.
Public-key cryptography, or RSA encryption, has simplified secure transactions of all times. This early form of encryption paved the way for Internet security, putting prime numbers at the heart of electronic commerce.
In 1978, three researchers discovered a way to scramble and unscramble coded messages using prime numbers. In fact, proof of the Riemann Hypothesis, based on Bernhard Riemann's theory about patterns in prime numbers, carries a $1 million prize from the Clay Mathematics Institute. The conjectures and theories put out by mathematicians at the time revolutionized math, and some have yet to be proven to this day. In the 17th century, mathematicians like Fermat, Euler and Gauss began to examine the patterns that exist within prime numbers. This sieve enables someone to come up with large quantities of prime numbers.īut during the Dark Ages, when intellect and science were suppressed, no further work was done with prime numbers. With these multiples crossed out, the only numbers that remain and are not crossed out are prime. So for this chart, you would cross out the multiples of 2, 3, 5 and 7. Since 6, 8, 9 and 10 are multiples of other numbers, you no longer need to worry about those multiples. For example, with a grid of 1 to 100, you would cross out the multiples of 2, 3, 4, 5, 6, 7, 8, 9, and 10, since 10 is the square root of 100. Eratosthenes put numbers in a grid, and then crossed out all multiples of numbers until the square root of the largest number in the grid is crossed out. This algorithm is one of the earliest algorithms ever written.
In 200 B.C., Eratosthenes created an algorithm that calculated prime numbers, known as the Sieve of Eratosthenes. This grid can be used as a Sieve of Eratosthenes if you were to cross out all of the numbers that are multiples of other numbers.
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