# Even and primes puzzle?

this is secret numbers that increase regularly, what is the order? If you like numbers, it will be fun.

1. $$2^3 \times224299$$
2. $$2^2 \times 3^2 \times 19 \times 3557$$
3. $$2 \times 5 \times 320647$$
4. $$2 \times 599 \times 3011$$
5. $$2 \times 29 \times 64283$$
6. $$2^3 \times 7 \times 11^3 \times 59$$
7. $$2^3 \times 7 \times 47 \times 1877$$
8. $$2^8 \times 19 \times 1229$$
9. $$2^2 \times 1639271$$
10. $$2^3 \times 17 \times 109 \times 569$$
11. $$2^3 \times 5^3 \times 17 \times 503$$
12. $$2^4 \times 3 \times 17 \times 29 \times 383$$
13. $$2^3 \times 233 \times 5051$$
14. $$2 \times 41 \times 127373$$
15. $$2^2 \times 3^3 \times 101141$$
16. $$2 \times 3 \times 5 \times 7^2 \times 7541$$
17. $$2^2 \times 3^3 \times 107621$$
18. $$2^4 \times 746723$$
19. $$2 \times 3 \times 2051923$$
20. $$2^2 \times 3 \times 11 \times 94433$$
21. $$2 \times 139 \times 46061$$
22. $$2 \times 83 \times 81847$$
23. $$2^2 \times 37 \times 99233$$
24. $$2 \times 5 \times 1522067$$
25. $$2^4 \times 1022963$$
26. ??
27. ??

$$26$$ th and $$27$$ th nubmer ?

• Can we be guaranteed that the factorization into primes isn't a red herring? That their actual products can safely be ignored? – Feryll Oct 1 '20 at 7:21
• yes it can be ignored, but it will certainly be an even number. – Mamu Oct 2 '20 at 18:51