Quote:
Originally Posted by jvriezen
For an arbitrary 13 digit number, its pretty unlikely to have only two prime factors and both 7 digits is even less likely. I'd suggest that these two numbers are worth further investigation.
Either the entire thing is a ruse and they chose the product of two relatively small primes just to lead to further useless lines of attack, or else the prime numbers are significant. Since its unlikely that the messages would directly encode into primes, maybe this:
1551037 = 117739th prime
6014357 = 413787th prime
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I strongly agree.
There are 586081 7 digit prime numbers. This means there are about 2*10^11 numbers with only 2 7 digit primes as factors. Only about 1 in 5 of these are 13 digits. There are about 10^14 13 digit numbers.
this means the probability of this as a random occurrence is about 1 in 250 (0.4%)
This is a large enough probability to encode data, but small enough probability to indicate significance.
117739 only has two factors excluding one and itself. They are both prime
281 (50th prime)
419 (81st prime)
This also seems improbable, only about 10,000 numbers with exclusively 3 digit prime factors exist. Not all of these will be 7 digits. The odds of one of these numbers having this characteristic will be about 1.6%.
People should look deeper into this.