The Twin primes constant is
0.6601618158468695739278121100145557784326233360 

References 
G. H. Hardy and E. M. Wright, An introduction to the theory of numbers,
Oxford University Press (several editions since 1938).

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These are known as the Hardy-Littlewood constants, 
for further explanations see the excellent account given by Steve Finch at

http://pauillac.inria.fr/algo/bsolve/hrdyltl/hrdyltl.html


Robert Joseph Harley computed further theses values about 
the Hardy-Littlewood conjecture.

from his home page...
http://pauillac.inria.fr/~harley/wnt.html


c_2 = 0.66016 18158 46869 57392 78121 10014 55577 84326 23360+ 
      c_3 = 0.63516 63546 04271 20720 66965 91272 52241 73420 65687+ 
      c_4 = 0.30749 48787 58327 09312 33544 86071 07685 30221 78520- 
      c_5 = 0.40987 48850 88236 47447 87812 12337 95527 78963 58013+ 
      c_6 = 0.18661 42973 58358 39665 69248 47944 18833 78400 73945- 
      c_7 = 0.36943 75103 86498 68932 31907 49876 75077 70553 72914- 
      c_8 = 0.23241 93345 86716 54620 61302 12670 66423 16017 58033- 
      c_9 = 0.12017 12067 74741 72146 99894 64638 47738 34654 94083- 
      c_10 = 0.04180 40508 12181 65710 39748 72842 46412 05882 81078+ 
      c_11 = 0.09453 08285 13547 15843 37971 55991 07208 84456 47523+ 
      c_12 = 0.03539 32598 44463 70442 74555 96801 94105 85290 48911- 
      c_13 = 0.11170 39095 63244 95377 12104 54656 08232 51503 03622+ 
      c_14 = 0.06284 46339 43607 42176 34598 50911 39350 53388 62666+ 
      c_15 = 0.02924 41621 25091 30867 18534 29424 46031 81891 89082- 
      c_16 = 0.00922 81011 53092 67664 26576 54374 72155 09035 30929+ 

































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