Table of Contents
Are there prime numbers in other bases?
So, for example, if you write your numbers base , there will be infinitely many primes ending with the relatively prime digits 1, 3, 5, 9, b, and d (where b is the digit for 11 and d the digit for 13), and there will be approximately the same number of primes ending with each of those digits.
Are prime numbers only base 10?
Prime numbers are prime, no matter what base you write them in. The definition of a prime number says nothing about base ten or decimal. The only requirement is that a prime number has exactly two factors, one and the number itself. 7 is still prime, even if it is written 111 (binary).
How many bases does a prime have?
Full reptend primes in various bases
Base | Full reptend primes |
---|---|
−24 | 13, 17, 19, 37, 41, 43, 47, 71, 89, 109, 113, 137, 139, 157, 163, 167, 181, 191, 211, 229, 233, 257, 263, 277. |
−23 | 2, 5, 7, 17, 19, 43, 67, 83, 89, 97, 107, 113, 137, 149, 181, 191, 199, 227, 229, 251, 263, 281, 283, 293, 337. |
How do you find cyclic numbers?
Form of cyclic numbers (Primes p that give cyclic numbers in base b are called full reptend primes or long primes in base b). For example, the case b = 10, p = 7 gives the cyclic number 142857, and the case b = 12, p = 5 gives the cyclic number 2497.
Is binary a prime number?
The first unique primes in binary (base 2) are: 3, 5, 7, 11, 13, 17, 19, 31, 41, 43, 73, 127, 151, 241, 257, 331, 337, 683….Binary unique primes.
Period length | Prime (written in decimal) | Prime (written in binary) |
---|---|---|
21 | 337 | 1 0101 0001 |
22 | 683 | 10 1010 1011 |
26 | 2,731 | 1010 1010 1011 |
42 | 5,419 | 1 0101 0010 1011 |
Is a prime number in the decimal system still a prime?
Is a prime number in the decimal system still a prime when converted to a different base? The base is a numbers symbology (display representation). A prime number is a prime by defination, irrespective of base.
Can a string of digits represent a prime number in another base?
There is a related question that might be causing you confusion (or may have caused you confusion), and that is: can a string of digits represent a prime in one base but a composite number in another base? The answer to that question is absolutely yes.
What is the number base of the largest prime numbers?
Prime numbers have nothing to do with number base. That is just a matter of representation. If you look at the Mersenne numbers, candidates for the largest known primes. They are all [math]2^p-1[/math], with [math]p[/math] a prime. If you look at their binary representation that is just a sequence of p ones.
How many primes end with a relatively prime number?
So, for example, if you write your numbers base , there will be infinitely many primes ending with the relatively prime digits 1, 3, 5, 9, b, and d (where b is the digit for 11 and d the digit for 13), and there will be approximately the same number of primes ending with each of those digits.