Sorry, no online dictionaries contain the exact phrase irreducible number.
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Reverse dictionary results:
1. atom
 2. element
3. basic
4. elementary
5. irreducibility
6. ato
7. conjugate
8. irrational
9. rational
10. incarceration
 11. quantum
12. base
13. basicity
14. cardinal
15. cent
16. core
17. coring
18. diploid
19. ether
20. family
 21. form
22. heavy
23. matter
24. meter
25. metering
26. metre
27. mole
28. monoploid
29. nine
30. ploidy
 31. pluralism
32. polyploid
33. positive
34. primary
35. pyrimidine
36. root
37. roots
38. rope
39. second
40. series

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