Long Period Prime/Examples

7 is a long period prime, since 1/7 = $0 \cdotp \dot 14285 \, \dot 7$ has period 6 = 7-1

17 is a long period prime, since 1/17 = $0 \cdotp \dot 05882 \, 35294 \, 11764 \, \dot 7$ has period 16 = 17-1

19 is a long period prime, since 1/19 = $0 \cdotp \dot 05263 \, 15789 \, 47368 \, 42 \dot 1$ has period 18 = 19-1

23 is a long period prime, since 1/23 = $0 \cdotp \dot 04347 \, 82608 \, 69565 \, 21739 \, 1 \dot 3$ has period 22 = 23-1

29 is a long period prime, since 1/29 = $0 \cdotp \dot 03448 \, 27586 \, 20689 \, 65517 \, 24137 \, 93 \dot 1$ has period 28 = 29-1

47 is a long period prime, since 1/47 = $0 \cdotp \dot 021276595744680851063829787234042553191489361 \dot 7$ has period 46 = 47-1

In contract,

2 is not a long period prime, since 1/2 = $0 \cdotp 5$ has no period

3 is not a long period prime, since 1/3 = $0 \cdotp \dot 3$ has period 1 < 3-1

5 is not a long period prime, since 1/5 = $0 \cdotp 2$ has no period

13 is not a long period prime, since 1/13 = $0 \cdotp \dot 07692 \dot 3$ has period 6 < 13-1

31 is not a long period prime, since 1/31 = $0 \cdotp \dot 03225 \, 80645 \, 1612 \dot 9$ has period 15 < 31-1

37 is not a long period prime, since 1/37 = $0 \cdotp \dot 02 \dot 7$ has period 3 < 37-1

41 is not a long period prime, since 1/41 = $0 \cdotp \dot 0243 \dot 9$ has period 5 < 41-1

43 is not a long period prime, since 1/43 = $0 \cdotp \dot 02325581395348837209 \dot 3$ has period 21 < 43-1