Loading ...
Sorry, an error occurred while loading the content.

Re: [PrimeNumbers] Adjacent composite numbers with pairs of adjacent prime factors

Expand Messages
  • Maximilian Hasler
    ... I found these other cases : [[403, 407, [13, 31], [11, 37]]] [[1003, 1007, [17, 59], [19, 53]]] [[110203, 110207, [193, 571], [191, 577]]] [[118003,
    Message 1 of 2 , Jun 15, 2012
    • 0 Attachment
      >>> > When you say "such cases", do you include the condition that they are
      >>> > semiprimes, or only that they have two pairs of adjacent prime factors?
      >> Yes, they must also be semiprimes.

      I found these other cases :

      [[403, 407, [13, 31], [11, 37]]]
      [[1003, 1007, [17, 59], [19, 53]]]
      [[110203, 110207, [193, 571], [191, 577]]]
      [[118003, 118007, [197, 599], [199, 593]]]
      [[418307, 418309, [557, 751], [563, 743]]]
      [[429491, 429493, [311, 1381], [307, 1399]]]
      [[439097, 439099, [577, 761], [571, 769]]]
      [[559003, 559007, [433, 1291], [431, 1297]]]
      [[1239869, 1239871, [907, 1367], [911, 1361]]]
      [[1887239, 1887241, [1249, 1511], [1259, 1499]]]
      [[2481463, 2481467, [1217, 2039], [1223, 2029]]]
      [[2502977, 2502979, [1367, 1831], [1373, 1823]]]
      [[3381403, 3381407, [1063, 3181], [1061, 3187]]]
      [[3693419, 3693421, [1567, 2357], [1571, 2351]]]
      [[5646257, 5646259, [1103, 5119], [1097, 5147]]]
      [[6120403, 6120407, [1427, 4289], [1429, 4283]]]
      [[6586003, 6586007, [1483, 4441], [1481, 4447]]]
      [[6954767, 6954769, [2287, 3041], [2281, 3049]]]
      [[7042661, 7042663, [967, 7283], [971, 7253]]]
      [[8350003, 8350007, [1667, 5009], [1669, 5003]]]
      [[11305093, 11305097, [1759, 6427], [1753, 6449]]]
      [[13083403, 13083407, [2087, 6269], [2089, 6263]]]
      [[13760203, 13760207, [2143, 6421], [2141, 6427]]]
      [[17297519, 17297521, [1699, 10181], [1697, 10193]]]
      [[21159419, 21159421, [1879, 11261], [1877, 11273]]]
      ...

      Maximilian

      PS:
      {e=[1,3,7,9,11]; forstep(a=10,9e9,10, for( i=2,#e,
      bigomega(a+e[i])==2 | (i++ & next);
      bigomega(a+e[i-1]) ==2 | next; f=factor(a+e[i-1])[,1];
      nextprime(f[1]+1)*precprime(vecmax(f)-1)==a+e[i]
      | precprime(f[1]-1)*nextprime(vecmax(f)+1)==a+e[i]
      | next; print([a+e[i-1],a+e[i],f~,factor(a+e[i])[,1]~]", ")))}
    Your message has been successfully submitted and would be delivered to recipients shortly.