Fun facts about prime numbers
These numbers are all primes:

-----
31
331
3331
33331
333331
3333331
33333331
-----

1444441
1777771
55555333
188888881
199999991
23456789
1234567891
9876543211
9876543217
12345678900001
123456737654321
123456797654321
12345678487654321
1234567894987654321
908070601
9080706050401
1231231237 -- ("123" repeated 3 times, then 7)
1481481481 -- ("148" repeated 3 times, then 1)
6666666661
9999999929
12121212121
14141414141
11111111113 -- ("1" repeated 10 times, then 3)
31111111111 -- ("3", then "1" repeated 10 times)
13131313133 -- ("13" repeated 5 times, then 3)
44444444441 -- ("4" repeated 10 times, then 1)
66666666667 -- ("6" repeated 10 times, then 7)
28282828283 -- ("28" repeated 5 times, then 3)
98989898981 -- ("98" repeated 5 times, then 1)
101111111111 -- ("10", then "1" repeated 10 times)
377777777777 -- ("3", then "7" repeated 11 times)
444444444443 -- ("4" repeated 11 times, then 3)
555555555551 -- ("5" repeated 11 times, then 1)
888888888887 -- ("8" repeated 11 times, then 7)
5555555555551 -- ("5" repeated 12 times, then 1)
7777777777771 -- ("7" repeated 12 times, then 1)
1666666666661
151515151515151
188888888888881
888888888888883 -- ("8" repeated 14 times, then 3)
1333333333333333 -- ("1", then "3" repeated 15 times)
101111111111111111 -- ("10", then "1" repeated 16 times)
222222222222222221 -- ("2" repeated 17 times, then 1)
333333333333333331 -- ("3" repeated 17 times, then 1)
666666666666666661 -- ("6" repeated 17 times, then 1)
1111111111111111111 -- ("1" repeated 19 times)
77777777777777777771 -- ("6" repeated 19 times, then 1)
666666666666666666661 -- ("6" repeated 20 times, then 1)
6666666666666666666661 -- ("6" repeated 21 times, then 1)
11111111111111111111111 -- ("1" repeated 23 times)
77777777777777777777771 -- ("7" repeated 22 times, then 1)
1313131313131313131313131 -- ("13" repeated 12 times, then 1)
4444444444444444444444444441 -- ("4" repeated 27 times, then 1)
6666666666666666666666666661 -- ("6" repeated 27 times, then 1)
7777777777777777777777777777771 -- ("7" repeated 30 times, then 1)
1717171717171717171717171717171 -- ("17" repeated 15 times, then 1)
999999999999999999999999999999991 -- ("9" repeated 32 times, then 1)
999999999999999999999999999999999999999999991 -- ("9" repeated 44 times, then 1)
-----

11!+1 = 39916801


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These are NOT primes:

1515151515151515151 = 267700723 × 5659870837 -- (2 distinct prime factors)
1818181818181818181 = 540905219 × 3361368599 -- (2 distinct prime factors)
199999999999999999991 = 282893137 ×706980742343 -- (2 distinct prime factors)
1919191919191919191919191 = 174551368897 × 10994997812503 -- (2 distinct prime factors)
6666666666666666666666661 = 161248624883 × 41344021826567 -- (2 distinct prime factors)
199999999999999999999999991 = 249051812839 × 803045750681969 -- (2 distinct prime factors)
121212121212121212121212121212121 = 326958513253 × 370726304099405593957 -- (2 distinct prime factors)
666666666666666666666666666666661 = 4050352743989 × 164594717745521180849 -- (2 distinct prime factors)
1010101010101010101010101010101010101 = 909090909090909091 × 1111111111111111111 (2 distinct prime factors)
1616161616161616161616161616161616161 = 431619980513 × 3744408713981995206392897 -- (2 distinct prime factors)
199999999999999999999999999999999999991 = 22869686025577 × 8745200951876820488652383 -- (2 distinct prime factors)
555555555555555555555555555555555555555551 = 284719837 × 1951235858411774644123428447858923 -- (2 distinct prime factors)
77777777777777777777777777777777777777777771 = 149931557774727697 × 518755216927972963426464443 -- (2 distinct prime factors)
99999999999999999999999999999999999999999999991 = 3701884489 × 27013268592563045799563304526436832319 -- (2 distinct prime factors)

9999999999999999999999999999999991 = 99999999999999997 × 100000000000000003 -- (2 distinct prime factors)


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