There are an infinite number of prime numbers. Many of them are large.
In fact ... since there are an infinite number of them, for any number you choose,
no matter how large it is, there are an infinite number of primes that are larger
than your number !
Here are the first 49 prime numbers that are larger than [1 billion] :
1,000,000,007
1,000,000,009
1,000,000,021
1,000,000,033
1,000,000,087
1,000,000,093
1,000,000,097
1,000,000,103
1,000,000,123
1,000,000,181
1,000,000,207
1,000,000,223
1,000,000,241
1,000,000,271
1,000,000,289
1,000,000,297
1,000,000,321
1,000,000,349
1,000,000,363
1,000,000,403
1,000,000,409
1,000,000,411
1,000,000,427
1,000,000,433
1,000,000,439
1,000,000,447
1,000,000,453
1,000,000,459
1,000,000,483
1,000,000,513
1,000,000,531
1,000,000,579
1,000,000,607
1,000,000,613
1,000,000,637
1,000,000,663
1,000,000,711
1,000,000,753
1,000,000,787
1,000,000,801
1,000,000,829
1,000,000,861
1,000,000,871
1,000,000,891
1,000,000,901
1,000,000,919
1,000,000,931
1,000,000,933
1,000,000,993
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There is no formula that will specifically give you a prime number and no non-prime number. Therefore, several large numbers are tested to see if they are primes, until a prime number is found.
The same way as with smaller numbers, it may take longer. Just keep dividing by prime numbers until all the factors are prime.
In part because the problem of finding large prime numbers isn't exactly trivial.
Data encryption, used for personal identification numbers (PINs) and for secure communications over the internet are based on very large prime numbers.
To determine the number of prime numbers between 1 and 8888888888888888888888888888888888888888888888, we can use the Prime Number Theorem. This theorem states that the density of prime numbers around a large number n is approximately 1/ln(n). Therefore, the number of prime numbers between 1 and 8888888888888888888888888888888888888888888888 can be estimated by dividing ln(8888888888888888888888888888888888888888888888) by ln(2), which gives approximately 1.33 x 10^27 prime numbers.