Successive prime differences

Successive prime differences is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The series of increasing prime numbers begins: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...

The task applies a filter to the series returning groups of successive primes, (s'primes), that differ from the next by a given value or values.

Example 1: Specifying that the difference between s'primes be 2 leads to the groups:

(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), ...

(Known as Twin primes or Prime pairs)

Example 2: Specifying more than one difference between s'primes leads to groups of size one greater than the number of differences. Differences of 2, 4 leads to the groups:

(5, 7, 11), (11, 13, 17), (17, 19, 23), (41, 43, 47), ....

In the first group 7 is two more than 5 and 11 is four more than 7; as well as 5, 7, and 11 being successive primes.

Task

• In each case use a list of primes less than 1_000_000
• For the following Differences show the first and last group, as well as the number of groups found:

1. Differences of 2.
2. Differences of 1.
3. Differences of 2, 2.
4. Differences of 2, 4.
5. Differences of 4, 2.
6. Differences of 6, 4, 2.

• Show output here.

Note: Generation of a list of primes is a secondary aspect of the task. Use of a built in function, well known library, or importing/use of prime generators from other Rosetta Code tasks is encouraged.

Python

Uses the Sympy library.

<lang python># https://docs.sympy.org/latest/index.html from sympy import Sieve

def nsuccprimes(count, mx):

   "return tuple of <count> successive primes <= mx (generator)"
   sieve = Sieve()
   sieve.extend(mx)
   primes = sieve._list
   return zip(*(primes[n:] for n in range(count)))

def check_value_diffs(diffs, values):

   "Differences between successive values given by successive items in diffs?"
   return all(v[1] - v[0] == d 
              for d, v in zip(diffs, zip(values, values[1:])))

def successive_primes(offsets=(2, ), primes_max=1_000_000):

   return (sp for sp in nsuccprimes(len(offsets) + 1, primes_max) 
           if check_value_diffs(offsets, sp))

if __name__ == '__main__':

   for offsets, mx in [((2,),      1_000_000), 
                       ((1,),      1_000_000),
                       ((2, 2),    1_000_000),
                       ((2, 4),    1_000_000),
                       ((4, 2),    1_000_000),
                       ((6, 4, 2), 1_000_000),
                      ]:
       print(f"## SETS OF {len(offsets)+1} SUCCESSIVE PRIMES <={mx:_} WITH "
             f"SUCCESSIVE DIFFERENCES OF {str(list(offsets))[1:-1]}")
       for count, last in enumerate(successive_primes(offsets, mx), 1):
           if count == 1:
               first = last
       print("  First group:", str(first)[1:-1])
       print("   Last group:", str(last)[1:-1])
       print("        Count:", count)</lang>

Output:

## SETS OF 2 SUCCESSIVE PRIMES <=1_000_000 WITH SUCCESSIVE DIFFERENCES OF 2
  First group: 3, 5
   Last group: 999959, 999961
        Count: 8169
## SETS OF 2 SUCCESSIVE PRIMES <=1_000_000 WITH SUCCESSIVE DIFFERENCES OF 1
  First group: 2, 3
   Last group: 2, 3
        Count: 1
## SETS OF 3 SUCCESSIVE PRIMES <=1_000_000 WITH SUCCESSIVE DIFFERENCES OF 2, 2
  First group: 3, 5, 7
   Last group: 3, 5, 7
        Count: 1
## SETS OF 3 SUCCESSIVE PRIMES <=1_000_000 WITH SUCCESSIVE DIFFERENCES OF 2, 4
  First group: 5, 7, 11
   Last group: 999431, 999433, 999437
        Count: 1393
## SETS OF 3 SUCCESSIVE PRIMES <=1_000_000 WITH SUCCESSIVE DIFFERENCES OF 4, 2
  First group: 7, 11, 13
   Last group: 997807, 997811, 997813
        Count: 1444
## SETS OF 4 SUCCESSIVE PRIMES <=1_000_000 WITH SUCCESSIVE DIFFERENCES OF 6, 4, 2
  First group: 31, 37, 41, 43
   Last group: 997141, 997147, 997151, 997153
        Count: 306