Metamath Proof Explorer
Description: The fifth Mersenne number M_5 = 31 is a prime number. (Contributed by AV, 17-Aug-2021)
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Ref |
Expression |
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Assertion |
m5prm |
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Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
3nn0 |
|
2 |
|
2nn0 |
|
3 |
|
1nn0 |
|
4 |
|
2exp5 |
|
5 |
|
3p1e4 |
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6 |
|
2m1e1 |
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7 |
1 2 3 4 5 6
|
decsubi |
|
8 |
|
31prm |
|
9 |
7 8
|
eqeltri |
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