0.7052301717918009651...

This number is neither prime nor composite.

                                                               0. 7052301717
9180096514 7431682888 2485137435 7763910915 4328192267 9138139197 8114800286
3586119051 9840274766 5925610800 7179413024 1628467791 2645127634 9299663226
7598728059 9996716792 5506124894 9356322341 8806948302 2468853419 6072922141
2205221537 4753776497 0396258762 9515977939 2679345195 4039019941 8322072857
8817970290 8727809538 7319904819 1260434112 8338252208 2180889762 8115375433
1390624110 6858988890 0601307081 0344698820 9670098318 2853682472 6465407922
7030430773 5209536552 9967950922 5012095838 6225330452 2624062298 2327181272

This is the sum (to 500 digits accuracy) of the reciprocals of the primorials. Note that the sum of the reciprocals of the primes diverges, the sum of the reciprocals of the primes to any power n>1 converges, and the sum of the reciprocals of the twin primes converges to Brun's constant. See Sloane AO64488. [Post]