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primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]
semiprimes=[]
triplets=[]
0.upto(primes.length - 1) do |x|
index = x
while index<(primes.length - 1) && (primes[x]*primes[index] < 2*primes[primes.length - 1])
semiprimes.push(primes[x]*primes[index])
index+=1
end
end
semiprimes.sort!
# find triplets
2.upto(semiprimes.length-1) do |x|
if semiprimes[x-2]+2 == semiprimes[x] && semiprimes[x-1]+1 == semiprimes[x]
triplets.push(semiprimes[x-2], semiprimes[x-1], semiprimes[x])
end
end
print triplets.join(", ")
Dead Cat wrote:So, does anyone else find this problem interesting and can anyone help with a proof of either hypothesis? Thanks in advance.
tomtom2357 wrote:That is probably about as difficult as the twin prime problem, which has not been solved yet.
Proginoskes wrote:tomtom2357 wrote:That is probably about as difficult as the twin prime problem, which has not been solved yet.
A new milestone has been reached, though: Terrence Tao recently proved that every odd number is the sum of at most five primes.
Proginoskes wrote:tomtom2357 wrote:That is probably about as difficult as the twin prime problem, which has not been solved yet.
A new milestone has been reached, though: Terrence Tao recently proved that every odd number is the sum of at most five primes.
xkcdfan wrote:Proginoskes wrote:tomtom2357 wrote:That is probably about as difficult as the twin prime problem, which has not been solved yet.
A new milestone has been reached, though: Terrence Tao recently proved that every odd number is the sum of at most five primes.
...41 is the sum of 2, 3, 5, 7, 11, and 13 though?
ameretrifle wrote:Magic space feudalism is therefore a viable idea.
tomtom2357 wrote:Proginoskes wrote:tomtom2357 wrote:That is probably about as difficult as the twin prime problem, which has not been solved yet.
A new milestone has been reached, though: Terrence Tao recently proved that every odd number is the sum of at most five primes.
Umm, isn't that the goldbach conjecture, and not the twin prime conjecture?
Proginoskes wrote:tomtom2357 wrote:Proginoskes wrote:tomtom2357 wrote:That is probably about as difficult as the twin prime problem, which has not been solved yet.
A new milestone has been reached, though: Terrence Tao recently proved that every odd number is the sum of at most five primes.
Umm, isn't that the goldbach conjecture, and not the twin prime conjecture?
Yeah. (Smacks head.) **** flu ...
Talith wrote:I can't see the latter case really throwing off any of the more important questions though, such as how any n-sequence is distributed or if there are infinitely many such sequences (unless some bizarre clustering happens around the squares of primes, which seems unlikely). When it comes to proving any of these results though, it may be easier to not throw out semiprimes which are squares.
tomtom2357 wrote:I have another question, are there any 7 consecutive 3-almost primes? The three even numbers, when divided by 2, form a semiprime triplet, so that narrows it down, but I haven't found any.
tomtom2357 wrote:So, are you sure those are the lowest 7-chains?
tomtom2357 wrote:Also, can there be two 7-chains that are next to each other (by this I mean the two chains are only separated by one multiple of 8)?
tomtom2357 wrote:Does any of this generalize to 2^{n}-1 chains of n-almost primes?
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