how to tell if a large number is prime or not

[logistic_guy]

here is the question

How to tell if $\displaystyle 87192883$ is a prime number or not?

$\displaystyle 87192883$ is not divisible by any prime numbers $\displaystyle \leq 97$

do this enough guarantee $\displaystyle 87192883$ is a prime number?

 

[blamocur]

here is the question

How to tell if $\displaystyle 87192883$ is a prime number or not?

$\displaystyle 87192883$ is not divisible by any prime numbers $\displaystyle \leq 97$

do this enough guarantee $\displaystyle 87192883$ is a prime number?

Of course it does not. 101*103 ( = 10403) has the same property but isn't prime.

 

[logistic_guy]

Of course it does not. 101*103 ( = 10403) has the same property but isn't prime.

thank

this mean without software it's almost impossible to tell if large number is prime. how could mathematicsians found large prime number without computer?

 

[lev888]

thank

this mean without software it's almost impossible to tell if large number is prime. how could mathematicsians found large prime number without computer?

"Since 1951 all the largest known primes have been found using these tests on computers.[a]"

Prime number - Wikipedia

en.wikipedia.org

 

[logistic_guy]

thank blamocur
thank lev888

i think prime number is tough