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You are not logged in. #1 20060219 21:44:56
Sum of the reciprocals of the squares of the prime numbersVery interesting prblem: IPBLE: Increasing Performance By Lowering Expectations. #2 20060219 21:46:53
Re: Sum of the reciprocals of the squares of the prime numbersWe know that: So 0<Sum<Pi^2/6 IPBLE: Increasing Performance By Lowering Expectations. #3 20060219 21:48:35
Re: Sum of the reciprocals of the squares of the prime numbersI'll try to make a program for the sum. IPBLE: Increasing Performance By Lowering Expectations. #4 20060219 21:51:33
Re: Sum of the reciprocals of the squares of the prime numbersHere's my program: Code:k = 100000; ss = 1000; Print["Initialization Done"]; Do[prt[i] = Prime[i], {i, 1, k}]; Print["Prime Geneneration Done"]; Do[prtsq[i] = prt[i]*prt[i], {i, 1, k}]; Print["Squaring Done"]; Do[thearr[i] = 1/prtsq[i], {i, 1, 100000}]; Print["Factorising Done"]; sum = 0; Do[sum += N[thearr[i], ss], {i, 1, 100000}]; Print["Sum = ", sum]; And here's what I get for the sum: IPBLE: Increasing Performance By Lowering Expectations. #5 20060219 21:52:49
Re: Sum of the reciprocals of the squares of the prime numbersIs this sum a irrational number? IPBLE: Increasing Performance By Lowering Expectations. #6 20060221 08:09:29
Re: Sum of the reciprocals of the squares of the prime numbersI get everything except the N and the ss usage. igloo myrtilles fourmis #7 20060223 01:54:48
Re: Sum of the reciprocals of the squares of the prime numbersIn Mathematica the "N(number,precise)" function gives the number with precisedigits after the demical point. IPBLE: Increasing Performance By Lowering Expectations. #8 20060223 04:55:10
Re: Sum of the reciprocals of the squares of the prime numbersAnd if Prime[] returns 0 if not prime, then why don't you get divide by zero error? igloo myrtilles fourmis #9 20060223 08:15:05
Re: Sum of the reciprocals of the squares of the prime numbersMaybe we could it "Krassi's Number" "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #10 20060301 05:15:37
Re: Sum of the reciprocals of the squares of the prime numbersFor John, not, PrimeQ[] is for testing whatever a number is prime. IPBLE: Increasing Performance By Lowering Expectations. #11 20060301 05:17:14
Re: Sum of the reciprocals of the squares of the prime numbersAnd for robya, it's actually a great idea to call it "Krassi's number". But it's not os scientific as "Geogiev's constant". IPBLE: Increasing Performance By Lowering Expectations. #12 20060302 06:33:03
Re: Sum of the reciprocals of the squares of the prime numbersOkay, now the program makes sense, thanks a lot. igloo myrtilles fourmis #13 20060303 10:17:52
Re: Sum of the reciprocals of the squares of the prime numbersMaybe the solution lies in the infinite pinotation format of the reimann zeta function Last edited by God (20060303 10:18:20) #14 20060303 23:15:49
Re: Sum of the reciprocals of the squares of the prime numbersWhat is that infinite pinotation? IPBLE: Increasing Performance By Lowering Expectations. 