### Basic Examples

Basic Examples

Here are the first ten pairs of cousin primes:

[10]

In[]:=

{{3,7},{7,11},{13,17},{19,23},{37,41},{43,47},{67,71},{79,83},{97,101},{103,107}}

Out[]=

Indeed, the differences are 4:

Differences/@%

In[]:=

{{4},{4},{4},{4},{4},{4},{4},{4},{4},{4}}

Out[]=

### Neat Examples

Neat Examples

The sum of the reciprocals of the primes diverges:

Sum[1/Prime@n,{n,∞}]

In[]:=

∞

∑

n

1

Prime[n]

Out[]=

The sum of the reciprocals of the cousin primes converges to a number around 1.673. Here is the sum of the reciprocals of the first 100,000 cousin primes:

Total1.Flatten@

[10^5]

In[]:=

1.51543

Out[]=

This is the last pair in that sum:

Last@

[10^5]

In[]:=

{18466729,18466733}

Out[]=