| Primorial
| |
|---|---|
Basic Info
| |
| Discovered by | N/A |
| Number of | Proven infinite |
| Description | Product of consecutive prime numbers |
| First Few | 2, 6, 30, 210, 2310 |
A primorial is a product of consecutive prime numbers, starting with the first prime, namely 2.
The primorial is created by multiplying subsequent prime numbers by themselves. For example, the primorial of 3 is 6, because 2*3=6. The primorial of 5 is 30, because 2*3*5=30.
Primorial differs from factorial in that primorial only multiplies prime numbers by themselves, while factorial multiplies all numbers by themselves.
Here are the 15 primorials of first prime numbers up to 50.[]
- 2 -> 2
- 3 -> 2*3=6
- 5 -> 2*3*5=30
- 7 -> 2*3*5*7 = 210
- 11 -> 2*3*5*7*11 = 2310
- 13 -> 2*3*5*7*11*13 = 30,030
- 17 -> 2*3*5*7*11*13*17 = 510,510
- 19 -> 2*3*5*7*11*13*17*19 = 9,699,690
- 23 -> 2*3*5*7*11*13*17*19*23 = 223,092,870
- 29 -> 2*3*5*7*11*13*17*19*23*29 = 6,469,693,230
- 31 -> 2*3*5*7*11*13*17*19*23*29*31 = 200,560,490,130
- 37 -> 2*3*5*7*11*13*17*19*23*29*31*37 = 7,420,738,134,810
- 41 -> 2*3*5*7*11*13*17*19*23*29*31*37*41 = 304,250,263,527,210
- 43 -> 2*3*5*7*11*13*17*19*23*29*31*37*41*43 = 13,082,761,331,670,030
- 47 -> 2*3*5*7*11*13*17*19*23*29*31*37*41*43*47 = 614,889,782,588,491,410