It is probably a useful method for finding large prime numbers and even more useful for
identifying the sequence of prime numbers in areas where thesequence of primes isn't known
(since the numbers are so big).
Consider the product 2*3*5*7*11.....p ie the product of all primes from to 2 to some prime
number p.
If q is a prime greater than p, than why is it likely that 2*3*5...p + q = a prime number.
For example consider the product 2*3*5*7=210. And let us consider the consecutive prime
numbers 11,13,17,19,23,29 and 31. We get
210+11=221
210+13=223
210+17=227
210+19=229
210+23=233
210+29=239
210+31=241
Notice that all of these numbers are prime except for 221. We can do a similar experiment
with say 2*3*5*7*11=2310, except this time use the primes 13,17,19,23,29,31,37
2310+13=2323
2310+17=2327
2310+19=2329
2310+23=2333
2310+29=2339
2310+31=2341
2310+37=2347
In this instance were not so lucky in that we only have 2333, 2339, 2341 and 2347 being
prime. Obviously this method gets worse the higher you go up. However what makes this
procedure useful, is that it enables you to determine consecutive prime numbers (this is
why you may have noticed that there are no prime numbers between the four primes written
above, or in the six primes in the first example).
Anyone here would like take a stab at why we get these results ?
2007-08-02
03:51:23
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4 answers
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asked by
BennnyVitalis123
1