| Line 1: |
Line 1: |
| | {{See also|Math and the Bible}} | | {{See also|Math and the Bible}} |
| | [[File:Eratosthenes.jpg|thumb|[[Eratosthenes]].]] | | [[File:Eratosthenes.jpg|thumb|[[Eratosthenes]].]] |
| − | A '''prime number''' is a [[natural number]] greater than 1 which is [[divisible]] by only 1 and itself. A prime number has only two [[factor]]s: 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13 .... The number 2 is the only even prime. | + | A '''prime number''' is a [[natural number]] greater than 1 which is [[divisible]] by only 1 and itself. A prime number has only two [[factor]]s: 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13 .... The number 2 is the only even prime. The [[Gospel of John]] is built on the prime number 7: seven [[miracle]]s, seven "I AM" declarations, and seven witnesses to the divinity of [[Jesus]]. |
| | | | |
| − | As the building block for all numbers, prime numbers have a [[spiritual]] quality that has fascinated [[mathematicians]] and others. Prime numbers are a great way to learn and teach [[math]], to improve mental acuity and focus, to fend off [[addiction]], and to understand great works such as the [[Bible]]. The two greatest unsolved mysteries in [[mathematics]] relate to prime numbers: why every even number is the sum of two primes ([[Goldbach's conjecture]]), and apparently there are [[infinity|infinitely]] many [[twin primes]]. It is unknown whether there are infinitely many [[Mersenne prime]]s. | + | '''''As the building block for all numbers, prime numbers have a [[spiritual]] quality that has fascinated [[mathematicians]] and others'''''. Prime numbers are a great way to learn and teach [[math]], to improve mental acuity and focus, to fend off [[addiction]], and to understand great works such as the [[Bible]]. The two greatest unsolved mysteries in [[mathematics]] relate to prime numbers: every even number greater than 2 is the sum of two primes ([[Goldbach's conjecture]]), and there are apparently [[infinity|infinitely]] many [[twin primes]]. There may be infinitely many [[Mersenne prime]]s. |
| | | | |
| | The [[multiplication of the loaves]] -- the only [[miracle]] described in all four [[Gospels]], and more than once in some Gospels, which suggests it happened more than once -- was always done with a prime number of loaves and fish (5 loaves and 2 fish, totaling 7, for the incidents described in {{bibleref|Mark|6|31-44}}, {{bibleref|Matthew|14|19}}, {{bibleref|Luke|9|13}}, and {{bibleref|John|6|9}}). When another such incident is described later in the [[Gospel of Matthew]], the multiplication occurs with another prime number-worth of loaves: 7. ''See'' {{bibleref|Matthew|15|34}}. Many [[biblical parables]] are tantalizing similar to prime numbers, such as [[The Parable of the Weeds]]. Acts 17:17, twice prime, is the midpoint of the [[New Testament]]. | | The [[multiplication of the loaves]] -- the only [[miracle]] described in all four [[Gospels]], and more than once in some Gospels, which suggests it happened more than once -- was always done with a prime number of loaves and fish (5 loaves and 2 fish, totaling 7, for the incidents described in {{bibleref|Mark|6|31-44}}, {{bibleref|Matthew|14|19}}, {{bibleref|Luke|9|13}}, and {{bibleref|John|6|9}}). When another such incident is described later in the [[Gospel of Matthew]], the multiplication occurs with another prime number-worth of loaves: 7. ''See'' {{bibleref|Matthew|15|34}}. Many [[biblical parables]] are tantalizing similar to prime numbers, such as [[The Parable of the Weeds]]. Acts 17:17, twice prime, is the midpoint of the [[New Testament]]. |
| Line 65: |
Line 65: |
| | For the integers, this definition is equivalent to the one stated above. However, in general the two definitions are not equivalent. The earlier definition is still important in rings and is given the name [[irreducibility]], since it literally states that the element cannot be broken into smaller pieces. | | For the integers, this definition is equivalent to the one stated above. However, in general the two definitions are not equivalent. The earlier definition is still important in rings and is given the name [[irreducibility]], since it literally states that the element cannot be broken into smaller pieces. |
| | | | |
| − | The preference for this alternate definition of "prime" is that this definition gives you unique [[factorization]] theorems analogous to the [[Fundamental Theorem of Arithmetic]]. For more information, consult an abstract algebra book<ref>'''Abstract Algebra: An Introduction''', Thomas Hungerford. Brooks Cole; 2 edition (1996)</ref> | + | The preference for this alternate definition of "prime" is that this definition gives you unique [[factorization]] theorems analogous to the [[Fundamental Theorem of Arithmetic]]. For more information, consult an abstract algebra book<ref>Thomas Hungerford, ''Abstract Algebra: An Introduction'', Brooks Cole: 2 edition (1996).</ref> |
| | | | |
| | ==Primality testing== | | ==Primality testing== |