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Output of compiled program newreadtest38a.out

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 are:

p = 990999999973 epsilon = 3.653183885026180310242468860377e-14 sigmarel = 49.196746580858837170307364573632
p = 991999999999 epsilon = 3.649367988977524534022013659376e-14 sigmarel = 49.198542882649387310383459409880
p = 992999999983 epsilon = 3.645559922508440300966127655797e-14 sigmarel = 49.200337590044634740764264493284
p = 993999999997 epsilon = 3.641759661414506257864442341368e-14 sigmarel = 49.202130207470124849483991253949
p = 994999999999 epsilon = 3.637967182022573332237327579364e-14 sigmarel = 49.203921257615048102004376570766
p = 995999999987 epsilon = 3.634182460603590021375694809873e-14 sigmarel = 49.205710415488945180061862050001
p = 996999999997 epsilon = 3.630405473381214673873020363065e-14 sigmarel = 49.207497790452109939479445745985
p = 997999999961 epsilon = 3.626636197067484207099474991832e-14 sigmarel = 49.209283257320235314096885215639
p = 998999999993 epsilon = 3.622874607783614393365893006510e-14 sigmarel = 49.211067028005100619569389489433
p = 999999999989 epsilon = 3.619120682566540114722976255853e-14 sigmarel = 49.212849006543337719956216007898

For the last value of ‘p’, 999999999989, the Robin upper bound on sigma(n)/n is given by:

? exp(Euler)*log(1000000442519.6083178943627706249117172)
%356 = 49.212850378644372402397034243512246754

where 1000000442519.6083178943627706249117172 is the natural logarithm of ‘n’ , with ‘n’ being the smallest colossally abundant number divisible by p=999999999989, was computed by an earlier program.

Is it true that:

49.212849006543337719956216007898 < 49.212850378644372402397034243512246754 ?

Yes it is.

In Keith Briggs’s paper:

“Abundant Numbers and the Riemann Hypothesis” (published in 2006) , he “tests” Robin’s criterion for superabundant and colossally abundant numbers, and evaluates numerically delta(n):= exp(gamma) log(log(n)) – sigma(n)/n,  for superabundant and colossally abundant numbers ‘n’ .There are plots relating to delta(n), also.

According to Briggs, the colossally abundant or CA numbers form a subset of the superabundant or SA numbers.

To be continued …

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Written by meditationatae

June 1, 2015 at 7:25 am

Posted in History

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