Sorry, no online dictionaries contain the exact phrase mersenne prime numbers.
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Reverse dictionary results:
1. prime number
 2. totient
3. sphenic
4. highwayman
5. atelier
6. mason
7. almanac
8. one
9. premier
10. two
 11. adam
12. ante
13. basic
14. canada
15. churchill
16. clark
17. cli
18. dos
19. eden
20. efficiency
 21. efficient
22. epitome
23. essential
24. fit
25. flower
26. grand
27. grans
28. hun
29. important
30. initial
 31. irrational
32. king
33. look
34. main
35. nine
36. old
37. past
38. primed
39. priming
40. principal

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You can look up the words in the phrase individually using these links:   mersenne ?   prime ?   numbers ?
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mers*to search for words beginning with mers, or
*bersto search for words ending with bers
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