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Previous Prime Number

Tool to search for prime numbers located before a number, or the nth previous prime number smaller than/inferior to a given number.

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Previous Prime Number -

Tag(s) : Arithmetics

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# Previous Prime Number

## Previous Prime Less than N Search

### How to calculate the previous prime number?

No mathematical formula allow to automatically calculate the prime number preceding any number N (less than N). dCode performs primality tests on numbers below the requested number until a prime number is found.

Example: The largest prime number that precedes 100 is 97

Example: The 10th prime number preceding 1000 is 937 (so there is a list of 9 prime numbers between 938 and 999 included)

The number $N$ must be a positive real number.

### How to find greatest primes with n digits ?

The largest number with $n$ digits is $10^n -1$ (that is always a multiple of 9), so the largest prime number with $n$ digits is the prime number that precedes $10^n-1$.

Example: The largest 4-digit number is $10^4 -1 = 10000-1 = 9999$ so the largest prime number with $n$ digits is the prime number preceding $10000$ that is $9973$.

The first 20 prime numbers in this list are: 7 (largest 1 digit prime), 97 (largest 2-digit prime), 997 (largest 3-digit prime), 9973, 99991, 999983, 9999991, 99999989, 999999937, 9999999967, 99999999977, 999999999989, 9999999999971, 99999999999973, 999999999999989, 9999999999999937, 99999999999999997, 999999999999999989, 9999999999999999961, 99999999999999999989 etc.

### What are twin primes numbers?

A prime number and the previous prime number are twins primes when their difference equals 2.

Example: 11 and 13 are called twins primes as 13-11 = 2.

## Source code

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