verify.sf

#!/usr/bin/ruby

# a(11) found m = 2138939853538560
# a(11) found m = 2526176995612160

# a(10) found m = 4009513558110720
# a(10) found m = 4196243334041600
# a(10) found m = 4250890925448960
# a(10) found m = 4264772670403840
# a(10) found m = 4694331125702400
# a(11) found m = 4729522651983360
# a(10) found m = 4790852606791680
# a(10) found m = 4996830163610880
# a(10) found m = 5101817933587200
# a(10) found m = 5264522678120960
# a(10) found m = 5431371042905600
# a(10) found m = 5523092697191680
# a(10) found m = 5525194236573440
# a(10) found m = 5727625856001280
# a(10) found m = 5778987687573760     (very close)
# a(10) found m = 5852062539581440
# a(10) found m = 5937381618013440
# a(10) found m = 5948907374009600
# a(10) found m = 5968911763043840
# a(11) found m = 6026433544209920
# a(10) found m = 6217329296404480
# a(10) found m = 6225694946248960
# a(10) found m = 6246007399831040
# a(10) found m = 6312132216947200
# a(10) found m = 6457158628226560
# a(10) found m = 6871581212112640
# a(10) found m = 6892136392410880
# a(10) found m = 6932779745830400
# a(10) found m = 6961627426082560
# a(10) found m = 7102360767040000
# a(10) found m = 7406828409708800
# a(10) found m = 7524854188308480
# a(10) found m = 7703508535374080
# a(10) found m = 7732872117268480
# a(10) found m = 7828103794118400
# a(10) found m = 7965222599924480
# a(9)  found m = 8012463159733760
# a(9)  found m = 8019012379031040
# a(9)  found m = 8024799172980480
# a(9)  found m = 8024968426908160
# a(9)  found m = 8028016589340160
# a(9)  found m = 8028450913889280

func chernick_carmichael_factors (n, m) {
    [6*m + 1, 12*m + 1, {|i| 2**i * 9*m + 1 }.map(1 .. n-2)...]
}

func is_chernick_carmichael (n, m) {
    (n == 2) ? (is_prime(6*m + 1) && is_prime(12*m + 1))
             : (is_prime(2**(n-2) * 9*m + 1) && __FUNC__(n-1, m))
}

var m = 8028450913889280
var a = chernick_carmichael_factors(12, m)

for k in (3..a.len) {
    var t = a.first(k).prod
    say t if t.is_carmichael
}

say ''

# If all three are true, then a(12) has been found
say is_chernick_carmichael(10, m)       # true if first 10 factors are prime
say is_chernick_carmichael(11, m)       # true if first 11 factors are prime
say is_chernick_carmichael(12, m)       # true if first 12 factors are prime

say ''

say chernick_carmichael_factors(12, m).map{.is_prime}
say chernick_carmichael_factors(11, m).last.factor
say chernick_carmichael_factors(12, m).last.factor

#~ say ''
#~ say chernick_carmichael_factors(11,m).prod.is_carmichael
#~ say chernick_carmichael_factors(12,m).prod.is_carmichael