123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100 |
- #!/usr/bin/ruby
- # Smallest overpseudoprime to base 2 (A141232) with n distinct prime factors.
- # https://oeis.org/A353409
- # Known terms:
- # 2047, 13421773, 14073748835533
- # Upper-bounds:
- # a(5) <= 1376414970248942474729
- # a(6) <= 48663264978548104646392577273
- # a(7) <= 294413417279041274238472403168164964689
- # a(8) <= 98117433931341406381352476618801951316878459720486433149
- # a(9) <= 1252977736815195675988249271013258909221812482895905512953752551821
- include("../../../factordb/auto.sf")
- var n = 7
- var psize = 10
- var from = 2647
- var upto = 3000
- say ":: Searching upper-bounds for n = #{n} in range #{from} .. #{upto}"
- var min = Hash()
- func check_combinations(f,n) {
- var count = 0
- var success = false
- f.combinations(n, {|*a|
- var t = a.prod
- if (t.is_strong_psp) {
- min{n} := Inf
- success = true
- if (t < min{n}) {
- say "\na(#{n}) <= #{t}\n"
- min{n} = t
- }
- }
- break if (++count > 1e6)
- })
- return success
- }
- var counter = 0
- for p in (primes(from, upto)) {
- if (++counter % 10 == 0) {
- say ":: Checking: p = #{p}"
- }
- for k in (p, 4*p, 12*p) {
- var f = factordb(2**k - 1).grep{ .len <= psize }.grep{.is_prime}.grep {|p| powmod(2, k, p) == 1 }.grep{|p| znorder(2,p) == k }
- say "[#{k}] Binomial: #{binomial(f.len, n)}" if (f.len >= n)
- var success = check_combinations(f, n)
- if (success) {
- say ":: Checking also the combinations for n = #{n+1}"
- check_combinations(f, n+1) &&
- check_combinations(f, n+2) &&
- check_combinations(f, n+3) &&
- check_combinations(f, n+4)
- }
- }
- }
- __END__
- a(5) <= 3223802185639011132549803
- a(5) <= 636607858967934928371769
- a(5) <= 145505063083208835861853
- a(5) <= 124250696089090697678753
- a(5) <= 79122810072725207031253
- a(5) <= 63018455673461680466449
- a(5) <= 8278905362357819790631
- a(5) <= 1376414970248942474729
- a(6) <= 6207602089353930933432401115757211526727413361
- a(6) <= 112236525927686091107643454350711622517
- a(6) <= 13264566429400773810375679971999741133
- a(6) <= 32245825439777493648426550929515449
- a(6) <= 721606983841657320586259138751241
- a(6) <= 44308853725126158640748255977121
- a(6) <= 157839641006967261025228640857
- a(6) <= 48663264978548104646392577273
- a(7) <= 294413417279041274238472403168164964689
- a(8) <= 98117433931341406381352476618801951316878459720486433149
- a(9) <= 1252977736815195675988249271013258909221812482895905512953752551821
|