And if some is researching on it. Please tell what have they found till now.
2007-05-27 21:07:31 · 20 answers · asked by C00L GαL 2 in Science & Mathematics ➔ Mathematics
Sorry but 9 isn't a prime, it is 3 x 3.
If you want to find out if a given number is prime or composite, the method used is called The Sieve of Eratosthenes. What you do is test whether the number is divisible by primes less than its square root.
If it does have two factors, then one of them will be smaller than the square root and one larger than it, so it is sufficient to test for numbers up to the square root: if you find no factors, then it is prime.
This implies that you know some low primes. Clearly 2 is the only even prime and 5 is the only number that ends in 5 that is prime, so all primes will end in 1 3 7 or 9 and you can eliminate numbers ending in 0 2 4 5 6 or 8 at a glance.
The first ten primes (ignoring 2 and 5) which you may need to use to divide into a given number are 3, 7, 11, 13, 17, 19, 23, 29, 31, 37. This will enable you to test numbers uo to 1680 for whether they are prime or not (1681 = 41^2)
Example: Is 143 a prime number? It is slightly less than the square root of 12 (12 x 12 = 144) so you need only test for divisibility by 3, 7 and 11.
The digits add up to 8 which is not divisible by 3 so it itself is not divisible by 3
You can tell at a glance that 7 x 20 = 140 so 143 is not divisble by 7.
However dividing by 11 gives 11 x 13 = 143 and therefore 143 is composite.
BIOGRAPHICAL NOTE
Eratosthenes, after whom this method is named, was a Greek scholar who lived in the 3rd Century BC and he was the first person to suggest the world (up till then believed to be flat) was a sphere and he managed to calculate what its radius and circumference were as well. He also devised a system of latitude and longitude and was for some years the librarian of the Library at Alexandria in Egypt.
2007-05-27 21:14:20 · answer #1 · answered by Anonymous · 5⤊ 3⤋
I'm sorry to say that but you have to remember all the prime numbers,at least inbetween 100. Inbetween 100 ther are 25 prime numbers. The first 30 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113. In mathematics, a prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. An infinitude of prime numbers exists, as demonstrated by Euclid in about 300 B.C..
2007-05-28 05:52:28 · answer #2 · answered by debdd03 2 · 0⤊ 0⤋
To say a thing like that is to confirm that the distinction between odd and even is more of a language concept than a numerical concept. You could also say that it is significant that among all the even numbers, 2 is the only prime one, compared with quite a lot of primes among the odd numbers. The real anomaly with 2 as a prime is because it is so small. For all other primes P, the number 1 behaves in a certain way relative to it, and the number P-1 behaves in a certain other way. When P is 2, the numbers 1 and P-1 are identical.
2016-05-19 21:15:35 · answer #3 · answered by ? 3 · 0⤊ 0⤋
(Step of 6+1) or (step of 6-1) is either "a prime number" or "a number having only prime number factors"!
If you want to do it by a matrix method do it like...
00, 01, 02. 03, 04, 05
06, 07, 08, 09, 10, 11
12, 13, 14, 15, 16, 17
18, 19, 20, 21, 22, 23
24, 25, 26, 27, 28, 29
30, 31, 32, 33, 34, 35
36, 37, 38, 39, 40, 41
42, 43, 44, 45, 46, 47,
48, 49, 50, 51, 52, 53
54, 55, 56, 57, 58, 59
60, 61, 63, 63, 64, 65
66, 67, 68, 69, 70, 71
72, 73, 74, 75, 76, 77
78, 79, 80, 81, 82, 83
84, 85, 86, 87, 88, 89
90, 91, 92, 93, 94, 95
96, 97, 98, 99, 99
You will find that column numbers '2' and '6' are iither prime numbers or 'numbers with prime number factor' alone! (Remember to start from zero onwards)!
Further column number '1' are "steps of 6" and rule stated above relates to said fact!
It is an ancient Indian knowledge!
Numbers ending with 5 and (49, 77 and 91) are numbers with 'prime number factor' alone!
With best regards!
2007-05-27 22:45:23 · answer #4 · answered by kkr 3 · 1⤊ 0⤋
For small numbers the standard technique is the sieve of eratosthenes - you take a grid of numbers cross out all multiples of two (other than two) - look at the first uncrossed out number (three), delete all multiples of three (other than three), then look for the next number - four is crossed out so the next number is five - cross out all multiples of five etc.
For a single number - to test if it is prime you have to divide by all prime factors less than the square root of the number - if there are no factors then the number is prime.
For very large numbers there is the Lucas Lehmer iterative test - this is used by GIMPS to find Mersene primes - to work out if 2^n-1 is prime - this is a collaborative project with a large prize for the first prime over 1million digits long - my computer is currently trying 2^37473181-1 and will take about a month to do it!
If an algorithm is found to determine primes quickly and easily the whole interent security system would collapse as most security is based on the difficulty of factorising the product of two very large primes!
2007-05-27 22:45:35 · answer #5 · answered by welcome news 6 · 0⤊ 0⤋
People have used sophisticated computer programs to generate prime numbers and they got some pretty big numbers. Mostly it is a brute force method that is used. For small numbers, the methods suggested in the other answers will be OK.
If you do a google or yahoo search, you will get a lot of information about prime numbers.
2007-05-27 21:34:57 · answer #6 · answered by Swamy 7 · 0⤊ 0⤋
A prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself.
Well this is what I do.................
Suppose the number you have got is "x"
Find out approximate value of square root of x
To illustrate here's an example:
Take the number 101
Nearest integer square root of 101 is 10
Now prime numbers below 10 are 2,3,5 and 7
Try dividing 101 by 2,3,5 and 7
Each time you'll get a remainder.
Thus 101 is a prime number.
This method is fool proof!
2007-05-27 21:20:47 · answer #7 · answered by Som™ 6 · 4⤊ 0⤋
Prime #= # that is divided only by 1 and itself
Is it divisible by...
2 is it even
3 are the sum of the digits divisible by 3
5 is the last digit a 0 or a 5
9 are the sum of the digits divisible by 9
10 is the last digit a 0
That's all the help I have.
2007-06-04 14:14:22 · answer #8 · answered by Mia 2 · 0⤊ 0⤋
the prime number divides only by itself and by 1.
i saw an answer earlier, 9 is not a prime number because it divides by 3 as well.
2007-05-27 21:22:50 · answer #9 · answered by Maddy 3 · 1⤊ 0⤋
A prime number is a number which is divisible only by 1 & by itself..
2007-06-04 06:14:04 · answer #10 · answered by dolly 2 · 0⤊ 0⤋