is 641 a prime number?

Question

prime and composite

Answer 1

yea

Answer 2

yes.

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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
127 131 137 139 149 151 157 163 167 173
179 181 191 193 197 199 211 223 227 229
233 239 241 251 257 263 269 271 277 281
283 293 307 311 313 317 331 337 347 349
353 359 367 373 379 383 389 397 401 409
419 421 431 433 439 443 449 457 461 463
467 479 487 491 499 503 509 521 523 541
547 557 563 569 571 577 587 593 599 601
607 613 617 619 631 641

Answer 3

Good question.
Yes, 641 is a prime number.

I tell the theory to find prime numbers:

It's one mathematicians are still trying to answer. The simplest method was developed by Eratosthenes in the 3rd century B.C. Here's how it works: Suppose we want to find all the prime numbers between 1 and 64. We write out a table of these numbers, and proceed as follows. 2 is the first integer greater than 1, so it is obviously prime. We now cross out all multiples of two. The next number that we haven't crossed out is 3. We circle it and cross out all its multiples. The next non-crossed-out number is 5, so we circle it and cross out all its multiples. We only have to do this for all numbers less than the square root of our upper limit (in this case sqrt(64)=8) since any composite number in the table must have at least one factor less than the square root of the upper limit. What's left after this process of elimination is all the prime numbers between 1 and 64.


Unfortunately, this method is rather time-consuming when the numbers you are looking for are much larger.

More Prime Number Theory
Mathematicians have developed a great amount of theory concerning prime numbers. Here's a taste of it:
Question: how far are prime numbers from each other? Sometimes, only 2 integers apart, like 41 and 43. Although there is a lot of evidence to suggest it, no one has proved that there are an infinite number of "twin primes."

In general, however, primes get more spread out as they get larger. By how much? In 1896 Charles de la Vallee-Poussin and Jacques Hadamard proved the Prime Number Theorem, which states:

Let Pr(x) be the number of prime numbers less than x. Then the ratio of Pr(x) to (x/ln(x)) approaches 1 as x grows without bound.

What this implies is that if n is a prime number, the distance to the next prime number is, on average, approximately ln(n).

The Goldbach Conjecture
In a letter to Leonard Euler in 1742, Christian Goldbach conjectured that every positive even integer greater than 2 can be written as the sum of two primes. Though computers have verified this up to a million, no proof has been given. Since Goldbach's time, however, his idea has been broken down into the 'strong' Goldbach conjecture - his original claim - and the 'weak' Goldbach conjecture, which claims that every odd number greater than 7 can be expressed as the sum of three odd primes. Try it and see!

Answer 4

Try dividing by 2, 3, 5, 7, 9, 11, 13, 17, 19 etc.

It does appear as if it is a prime number.

Answer 5

since 26 * 26 > 641
you only have to check the prime numbers less than 26
2, 3, 5, 7, 11, 13, 17, 19, 23

Answer 6

641 is a prime number

Answer 7

641 is a prime

Answer 8

There is a good way to determine any primitive number :
assume an arbitrary number "N" . then calculate Sqrt(N). then Davide N to all of the primitive numbers smaller than Sqrt(N). if any divisions could be done, N isn't prime.
In this example:
Sqrt(641) ~ 25.3
then you should divide 641 by 2,3,5,7,11,13,17,19,23
none of them will give you an integer answer,so thats primitive.
Now you can determine any primitive number
Good luck

Answer 9

An integer greater than 1 but cannot be evenly divided by any number other than itself is a prime number. So take a little calculation and you can answer a lot of similar question in the future.

Answer 10

yup. 641 is the prime number.

Answer 11

Yes, it is.

It is a Sophie Germain prime, meaning 2p + 1 is also prime. It's also a Proth prime, and a Chen prime.