prime differences

[AntonioLao]

Paul Erdös (1913-96) Hungarian mathematician published more than 1500 papers, jointly or solo. He was always looking for elegant and simple solutions to complex problems. The following conjecture on limited prime differences can be attributed to his life-long investigations for prime numbers.

Given a prime number, p, every even number less than p can be expressed as the difference of two primes less than or equal to p. For example, if p=23 then 2=19-17, 4=17-13, 6=17-11, 8=19-11, 10=17-7, 12=19-7, 14=19-5, 16=19-3, 18=23-5, and 20=23-3. Obviously, this scheme failed for the even number 22 unless 1 is defined as a prime. However, if this is generalized to the group number of p then it works for all even numbers. The conjecture restated as: There are infinitely many primes, p, such that every even number belonging to the group number G(p)-1 can be expressed as the difference of two primes less than or equal to p. This can be proved algorithmically using simply a sieve of Diophantus.

[mkirkpatrick]

We are both in our prime Antonio,the only real difference is that you are in Texas and
still working for a living,and I am in Turkey and retired! I like numbers and years ago
studied numerology,now though I see just 1 and 0 with nothing real inbetween?



regards michael.

[AntonioLao]

I would consider myself as a deficient semiprime which still needed a few prime factorizations to become an absolute prime.

[mkirkpatrick]

I would consider myself as a deficient semiprime which still needed a few prime factorizations to become an absolute prime.

Three years have now gone by my friend,you are now in you prime and ready to retire!


regards michael.

[AntonioLao]

Actually I'm retired. But I'm having problem receiving my benefits. Also, I'm allow to work for income not to exceed 14 grands.

[mkirkpatrick]

Actually I'm retired. But I'm having problem receiving my benefits. Also, I'm allow to work for income not to exceed 14 grands.

Thats good news that you have retired,not so good that you are having problems recieving them,hope it soon gets sorted for you Antonio,have you found a part time job yet then?

regards michael.

[AntonioLao]

I'm still contracted to the public school system in this city to do part-timing as a substitute math teacher.

[mkirkpatrick]

I'm still contracted to the public school system in this city to do part-timing as a substitute math teacher.

That's great at least you have an income coming in until they sort out your pension benefit.Bet if I was in your class I would pass all my exams!


regards michael.

[AntonioLao]

Actually, substitutes dont really teach. They just babysit. Easy money if ever they call me to sub for the subjects (math, science, chemistry, but not biology) I want to do,

[mkirkpatrick]

Actually, substitutes dont really teach. They just babysit. Easy money if ever they call me to sub for the subjects (math, science, chemistry, but not biology) I want to do,

Well at least you get a paycheck for babysitting some potential boffins of the future!


regards michael.