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CTK Exchange
Cman
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Oct-14-02, 09:11 PM (EST) |
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"proving prime number?"
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Hello: I just visited your site. I had a simply question to ask? I know 1321 is a prime number? But, is there a
formula or method to prove it? I find it hard to figure out the formulas posted on the web. |
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japam
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Feb-24-04, 07:15 PM (EST) |
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4. "RE: proving prime number?"
In response to message #1
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i will give you this hint to your problemlook at this
01 *21= 21------------------0+2=2
11 *11= 121-----------------1+1=2
21 *01= 21------------------2+0=2
31 *91= 2821----------------3+9=12
41 *81= 3321----------------4+8=12
51 *71= 3621----------------5+7=12
61 *61= 3721----------------6+6=12 |
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RicBrad
Member since Nov-16-01
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Oct-15-02, 10:31 AM (EST) |
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2. "RE: proving prime number?"
In response to message #0
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There is no really easy way to find if a number is prime, especially by hand. For small numbers, with a computer, the simplest method is trial division (up to sqrt(n)). For very small numbers (in computing terms), such as this one, you might like to know Wilson's Theorem: A number p is prime if, and only if, (p - 1)! = -1 (mod p) In this case: (p - 1)! = 1320! = 7051433211515310579887386749........00000000000
= approx 103551, and ending with 328 zeros
= 1320 (mod 1321) = -1 (mod 1321) So it is prime. As I said, this might be a little tricky to do by hand.  Rich p.s. I tried to put in all 3551 digits, but the form wouldn't let me preview it... lol
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noname
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Oct-15-02, 10:31 AM (EST) |
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3. "RE: proving prime number?"
In response to message #0
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to prove a number is prime, you must prove that it cannot be divided by any prime number inferiour to its square root.
Here, (1321)^(1/2) must be about 40 so check out that
for k in {2,3,5,7,11,13,17,19,23,29,31,37} you have 1321/k not an integer.
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