Euclid primes from 1 to 10000

p_n# + 1
Unsolved problem : Are there an infinite number of prime Euclid numbers ?
3
7
31
211
2311
Euclid numbers
3 = 2 + 1
prime number
7 = 3*2 + 1
prime number
31 = 5*3*2 + 1
prime number
211 = 7*5*3*2 + 1
prime number
2311 = 11*7*5*3*2 + 1
prime number
30031 = 13*11*7*5*3*2 + 1
= 59 * 509
510511 = 17*13*11*7*5*3*2 + 1
= 19 * 97 * 277
9699691 = 19*17*13*11*7*5*3*2 + 1
= 347 * 27953
223092871 = 23*19*17*13*11*7*5*3*2 + 1
= 317 * 703763
6469693231 = 29*23*19*17*13*11*7*5*3*2 + 1
= 331 * 571 * 34231
200560490131 = 31*29*23*19*17*13*11*7*5*3*2 + 1
prime number
7420738134811 = 37*31*29*23*19*17*13*11*7*5*3*2 + 1
= 181 * 60611 * 676421
304250263527211 = 41*37*31*29*23*19*17*13*11*7*5*3*2 + 1
= 61 * 450451 * 11072701
13082761331670031 = 43*41*37*31*29*23*19*17*13*11*7*5*3*2 + 1
= 167 * 78339888213593
614889782588491411 = 47*43*41*37*31*29*23*19*17*13*11*7*5*3*2 + 1
= 953 * 46727 * 13808181181
32589158477190044731 = 53*47*43*41*37*31*29*23*19*17*13*11*7*5*3*2 + 1
= 73 * 139 * 173 * 18564761860301