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sachinism
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Is it possible to write the 2010 numbers from 1 a 2010 in some order so that the
6933 digit number you get is prime?
6933 digit number you get is prime?
Bill Simpson said:2010!=3n+1.
Wizlem said:I get 4/10*2009! ways to do it. It helps to know the 6933 digit is the last digit.
For instance if you write the numbers from 1 to 3 in some order you can get 123 132 213 231 312 or 321.
Bill Simpson said:For numbers m up to 301 a prime formed from the concatenation of the digits of a permutation of the numbers 1...m can be found in the first 7 factorial permutations I inspect for all numbers of the form 3n+1 except for 160, 172, 271, 283 and 298 and for none of the numbers of the form 3n or 3n+2. For 160 no "prime permutation" was found in the first 2924903 permutations inspected, but I expect that with more permutations inspected that a prime will be found.
hamster143 said:It would do you good to observe that all six of these permutations are divisible by 3.
You could then try to generalize that observation.
Yes, it is possible to find new prime numbers in any year, including 2010. Prime numbers are infinite, meaning there is no limit to the number of primes that can be found.
There are several methods for finding prime numbers, including using a sieve algorithm, checking divisibility by all numbers up to the square root of the number, and using complex mathematical formulas. These methods can be time-consuming and require advanced mathematical knowledge.
While there are some patterns and trends in prime numbers, such as the fact that all primes (except 2 and 3) are odd numbers, they ultimately appear to be random. This is one of the reasons why finding new prime numbers can be a difficult and ongoing pursuit for mathematicians.
Prime numbers have many practical applications, such as in cryptography and computer security. They also play a key role in number theory and have been studied for centuries by mathematicians. Additionally, finding new prime numbers helps expand our understanding of mathematics and can lead to the discovery of new mathematical concepts.
As mentioned before, prime numbers are infinite, so there is no largest prime number. However, as of 2020, the largest known prime number has over 24 million digits and was discovered through a distributed computing project called the Great Internet Mersenne Prime Search (GIMPS).