Something that should be straightforward: difference of 6, product of 3127

Simonsky

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Jul 4, 2017
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128
Yet another question stumping (UK cricket related metaphor?) me which is rather depressing and a sign of limited progress in being able to think mathematically.

Two consecutive prime numbers have a difference of 6 and a product of 3127 -find the numbers.

Pathetic as it is, all I can seem to do is write ab = 3127 and b-a = 6 and can't seem to get my brain to budge and think laterally, it just seems locked!

Anyone give me a gentle nudge or pointer without revealing too much? Thanks.

Hang on, I think I'm experiencing a 'brain thaw'...... perhaps substitution required???.......so: if a = b-6 then ab = b(b-6) = b^2 -6b = 3127

so b^2 - 6b -3127 = 0 and using the formula one gets b=59 so a - 53.

That helped, working out live on this site - perhaps I should delete it now I've got the answer .....Oh well maybe I'll leave the post as an example of how the brain can suddenly 'unlock'.
 
Yet another question stumping (UK cricket related metaphor?) me which is rather depressing and a sign of limited progress in being able to think mathematically.

Two consecutive prime numbers have a difference of 6 and a product of 3127 -find the numbers.

Pathetic as it is, all I can seem to do is write ab = 3127 and b-a = 6 and can't seem to get my brain to budge and think laterally, it just seems locked!

Anyone give me a gentle nudge or pointer without revealing too much? Thanks.

Hang on, I think I'm experiencing a 'brain thaw'...... perhaps substitution required???.......so: if a = b-6 then ab = b(b-6) = b^2 -6b = 3127

so b^2 - 6b -3127 = 0 and using the formula one gets b=59 so a - 53.

That helped, working out live on this site - perhaps I should delete it now I've got the answer .....Oh well maybe I'll leave the post as an example of how the brain can suddenly 'unlock'.

Please do not delete. Excellent example. Sometimes, it just helps to talk it out. Good work. What you did was recast the problem, from one of maybe Number Theory to one of Elementary Algebra. This sort of recasting is a most valuable tool for finding solutions to problems. Thanks for the demonstration.
 
Please do not delete. Excellent example. Sometimes, it just helps to talk it out. Good work. What you did was recast the problem, from one of maybe Number Theory to one of Elementary Algebra. This sort of recasting is a most valuable tool for finding solutions to problems. Thanks for the demonstration.

Thanks. I might do more of this, then. I'm self-educating, so working from books on my own which means I can easily get stuck and need to bounce of others on this excellent site.

I'm also interested in the psychological/cognitive aspects of the learning process and why I (or others) find thinking fluidly elusive.

Maybe it would be useful to have a special thread on learning issues? - there are some experienced maths pedagogues on this site who probably have a lot of insights in this are.
 
Notice, by the way, that the two conditions, b- a= 6 and ab= 3127, are sufficient to determine a and b. The fact that "a and b are prime" is just happenstance and not necessary to the problem.
 
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