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

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 <code>2</code> leads to the groups: 
:<code>(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), ...</code> <br>
(Known as [[wp:Twin prime|Twin primes]] or [https://oeis.org/A077800 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 <code>2, 4</code> leads to the groups: 
:<code>(5, 7, 11), (11, 13, 17), (17, 19, 23), (41, 43, 47), ...</code>. <br>
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. 
Differences are checked in the order of the values given, (differences of <code>4, 2</code> would give different groups entirely).

;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:
:# Differences of <code>2</code>.
:# Differences of <code>1</code>.
:# Differences of <code>2, 2</code>.
:# Differences of <code>2, 4</code>.
:# Differences of <code>4, 2</code>.
:# Differences of <code>6, 4, 2</code>.
* Show output here.

<br>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 [[Sieve of Eratosthenes|Rosetta Code tasks]] is encouraged.

;references
:#https://pdfs.semanticscholar.org/78a1/7349819304863ae061df88dbcb26b4908f03.pdf
:#https://www.primepuzzles.net/puzzles/puzz_011.htm
:#https://matheplanet.de/matheplanet/nuke/html/viewtopic.php?topic=232720&start=0