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modular:02_primes [2014/01/31 23:43] marje |
modular:02_primes [2014/01/31 23:56] marje |
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| These divisors are $1$, which divides all natural numbers, and the number $n$ itself. | These divisors are $1$, which divides all natural numbers, and the number $n$ itself. | ||
| - | Anyone can easily recall some smallest prime numbers, e.g., $2,3,5,7,11,13,17$ etc. Although in general, determining whether a given (large) number is prime can be a very resource consuming. Also the location of primes among integers can not be easily computed, however there are many interesting patters, see e.g. [[http://en.wikipedia.org/wiki/Ulam_spiral|Ulam spiral]] and [[http://en.wikipedia.org/wiki/Prime_number_theorem|Prime number theorem]]. | + | Anyone can easily recall some smallest prime numbers, e.g., $2,3,5,7,11,13,17$ etc. Although in general, determining whether a given (large) number is prime can be a very resource consuming. Also, the location of primes among integers can not be easily computed, however there are many interesting patters, see e.g. [[http://en.wikipedia.org/wiki/Ulam_spiral|Ulam spiral]] and [[http://en.wikipedia.org/wiki/Prime_number_theorem|Prime number theorem]]. |
| <WRAP task> | <WRAP task> | ||
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| $3675=2^0 \cdot 3^1 \cdot 5^2 \cdot 7^2 $. | $3675=2^0 \cdot 3^1 \cdot 5^2 \cdot 7^2 $. | ||
| - | Note that there can be primes $p_i$ which do not divide $n$ and thus their power $e_i=0$. | + | Note that there can be primes $p_i$ which do not divide $n$ and thus their power $e_i=0$ written to the end of the prime factorisation if needed. |
| <WRAP task> | <WRAP task> | ||