| 1 | What is the arithmetic progression? | |
| 2 | Subsistence only increases in an arithmetic ratio. | |
| 3 | It has been proved that the primes contain arbitrarily long arithmetic progressions. | |
| 4 | Every large odd integer can be represeted as the sum of three primes which take from arithmetic progressions. | |
| 5 | Population, when unchecked, increases in a geometric ratio. Subsistence increases in an arithmetical ratio. |