= = = EISENMANN PRIMES = = =
An Eisenmann number is a number of the form A * 10^B - 1, where A and B are integers such that 0 < A < 10 and B > 0. Some examples of Eisenmann numbers are 19, 29, 39, 49, 499, and 4,999.
An Eisenmann prime is an Eisenmann number which is prime.
Eisenmann primes are my favorite numbers. I have been using a custom made program to search for Eisenmann primes. The program uses the GMP arithmetic library and the Miller-Rabin primality test. For each candidate I test a large number of bases to determine primality with an extremely high degree of confidence. In particular, the number of bases I test for each candidate is the number of binary digits in the candidate.
Below are all of the Eisenmann primes I have found:
2 * 10^1 - 1
3 * 10^1 - 1
6 * 10^1 - 1
8 * 10^1 - 1
9 * 10^1 - 1
2 * 10^2 - 1
5 * 10^2 - 1
6 * 10^2 - 1
2 * 10^3 - 1
3 * 10^3 - 1
5 * 10^3 - 1
9 * 10^3 - 1
5 * 10^4 - 1
6 * 10^4 - 1
8 * 10^4 - 1
2 * 10^5 - 1
6 * 10^5 - 1
8 * 10^5 - 1
3 * 10^6 - 1
5 * 10^6 - 1
2 * 10^7 - 1
3 * 10^7 - 1
6 * 10^7 - 1
9 * 10^7 - 1
8 * 10^8 - 1
6 * 10^10 - 1
8 * 10^10 - 1
6 * 10^13 - 1
5 * 10^14 - 1
3 * 10^19 - 1
9 * 10^19 - 1
6 * 10^22 - 1
6 * 10^23 - 1
8 * 10^25 - 1
2 * 10^26 - 1
2 * 10^27 - 1
3 * 10^27 - 1
6 * 10^28 - 1
9 * 10^29 - 1
6 * 10^34 - 1
9 * 10^37 - 1
6 * 10^40 - 1
3 * 10^43 - 1
8 * 10^49 - 1
2 * 10^53 - 1
5 * 10^54 - 1
3 * 10^55 - 1
6 * 10^61 - 1
6 * 10^73 - 1
8 * 10^76 - 1
9 * 10^93 - 1
8 * 10^128 - 1
2 * 10^147 - 1
8 * 10^175 - 1
3 * 10^207 - 1
5 * 10^210 - 1
2 * 10^236 - 1
8 * 10^238 - 1
2 * 10^248 - 1
6 * 10^361 - 1
2 * 10^386 - 1
5 * 10^390 - 1
2 * 10^401 - 1
6 * 10^490 - 1
2 * 10^546 - 1
8 * 10^550 - 1
5 * 10^594 - 1
6 * 10^613 - 1
2 * 10^785 - 1
8 * 10^796 - 1
9 * 10^935 - 1
8 * 10^1219 - 1
3 * 10^1311 - 1
2 * 10^1325 - 1
6 * 10^1624 - 1
2 * 10^1755 - 1
6 * 10^2000 - 1
8 * 10^2012 - 1
8 * 10^2846 - 1
2 * 10^2906 - 1
6 * 10^2994 - 1
2 * 10^3020 - 1
3 * 10^3204 - 1
5 * 10^3460 - 1
6 * 10^4301 - 1
6 * 10^4332 - 1
5 * 10^5028 - 1
5 * 10^5219 - 1
5 * 10^5332 - 1
2 * 10^5407 - 1
2 * 10^5697 - 1
2 * 10^5969 - 1
3 * 10^7050 - 1
2 * 10^7517 - 1
5 * 10^8072 - 1
9 * 10^8415 - 1
3 * 10^9439 - 1
9 * 10^9631 - 1
9 * 10^11143 - 1
8 * 10^11336 - 1
2 * 10^15749 - 1