Month: June 2015

Reminder:  For a colossally abundant number n, with n > 5040, one can define delta(n) := exp(gamma)*log(log(n)) – sigma(n)/n               [Briggs, def. 4-2, page 254 ] . This is as in the paper by Keith Briggs, Briggs, K.,  2006, “Abundant Numbers and the Riemann Hypothesis“. sigma(.) is the sum of… Continue reading Computations on 8000 colossally abundant numbers out to exp(exp(29.710462))

For the record, the source code, compiled code, table of the first 1,000,000 primes and files used to store intermediate results are held in four directories: [david2@localhost ~]$ pwd /home/david2 (above is my home directory on my computer, /home/david2/ About below: Below, the command `ls -l eratosthenes1[5678]’ has the system list all files and directories… Continue reading Memo on extending the CA number calculations out to exp(exp(29))

Please compare preceding graph with that in Figure 3 (Bottom) from: Keith Briggs, “Abundant Numbers and the Riemann Hypothesis”, Experiment. Math., Volume 15, Issue 2 (2006), 251-256.

Please compare Briggs [2006] ,  “FIGURE 3” , bottom, “Deviation of log(δ) from a best-fit line at CA numbers” x = log(log(n)), y = deviation, n = a CA number (below). X  ,  Y 20.72328036823640753487 0.01928812277933495504 21.41641568589025523946 0.00467503027989789420 21.82188330500718220766 -0.01857803449402955915 22.10956936787925566329 -0.01442664754704527536 22.33270529973400392535 -0.00498884443497253787 22.51503213252200525579 0.01088285328216521960 22.66918125498666494740 -0.01429344711957802149 22.80270969051157491845 0.01583390785426878241 22.92049377575773232772 0.00913729536799508871 23.02585918471295815829 -0.00556723123961362092 23.12116444840649185777… Continue reading Output of newreadtest48a.out (compiled code of newreadtest48a.c)

#include <stdio.h> #include <quadmath.h> int main(void) { int j; long lastprime; __float128 thesigmas[1000]; __float128 thelogs[1000]; char buf1[100]; char buf2[100]; __float128 epsilon; __float128 ca_log; __float128 sigma; __float128 y; __float128 gamma = 0.57721566490153286060651209008240243104Q; __float128 f2; __float128 delta; FILE *in1; FILE *in2; f2 = (__float128) 2; in1 = fopen(“/home/david2/eratosthenes10/June02/newreadtest28bb.txt”, “r”); in2= fopen(“/home/david2/eratosthenes10/June02/newreadtest38bb.txt”, “r”); for(j=0; j<1000; j++) { fscanf(in1,… Continue reading cat newreadtest48a.c

First, I get the shell history: 1419 gcc -lquadmath -o newreadtest38a.out newreadtest38a.c compile newreadtest38a.c to executable newreadtest38a.out 1420 ./newreadtest38a.out run the executable newreadtest38a.out 1421 tail newreadtest28a.txt display last 10 lines of newreadtest28a.txt 1422 ./newreadtest38a.out > newreadtest38a.txt run the executable newreadtest38a.out and redirect the output to the file newreadtest38a.txt . The last 10 lines of newreadtest38a.txt… Continue reading Output of compiled program newreadtest38a.out

$ tail -50 newreadtest38a.txt | head -20 p = 703999999991 epsilon = 5.206936379639033740419105966666e-14 sigmarel = 48.587733476088662511652037486990 p = 704999999993 epsilon = 5.199280123147372689423924155999e-14 sigmarel = 48.590261677681938981087528080719 p = 705999999989 epsilon = 5.191645966780712764165758085166e-14 sigmarel = 48.592786209376990418736119033969 p = 706999999903 epsilon = 5.184033816133774783104201567653e-14 sigmarel = 48.595306970527793061343313912681 p = 707999999983 epsilon = 5.176443574880798963089930016747e-14 sigmarel = 48.597824150211233639402505984025 p = 708999999997… Continue reading About newreadtest38a.c

[david2@localhost eratosthenes10]$ pwd /home/david2/eratosthenes10 cat newreadtest38a.c #include <stdio.h> #include <quadmath.h> int smallp[1000000]; int main(void) { int j; long low, high, count, lastprime; __float128 sigmarelative[1000]; char buf1[100]; char buf2[100]; __float128 r; __float128 epsilon; __float128 var01; __float128 var02; __float128 var03; __float128 var04; __float128 var05; __float128 var06; __float128 var07; int power2; int exponent; long p; long smallprime; __float128… Continue reading cat newreadtest38a.c