Task: Successive prime differences
C#: using System;
using System.Collections.Generic;
using static System.Linq.Enumerable;

public static class SuccessivePrimeDifferences {

    public static void Main() {
        var primes = GeneratePrimes(1_000_000).ToList();
        foreach (var d in new[] {
            new [] { 2 },
            new [] { 1 },
            new [] { 2, 2 },
            new [] { 2, 4 },
            new [] { 4, 2 },
            new [] { 6, 4, 2 },
        }) {
            IEnumerable<int> first = null, last = null;
            int count = 0;
            foreach (var grp in FindDifferenceGroups(d)) {
                if (first == null) first = grp;
                last = grp;
                count++;
            }
            Console.WriteLine($"{$"({string.Join(", ", first)})"}, {$"({string.Join(", ", last)})"}, {count}");
        }

        IEnumerable<IEnumerable<int>> FindDifferenceGroups(int[] diffs) {
            for (int pi = diffs.Length; pi < primes.Count; pi++)
                if (Range(0, diffs.Length).All(di => primes[pi-diffs.Length+di+1] - primes[pi-diffs.Length+di] == diffs[di]))
                    yield return Range(pi - diffs.Length, diffs.Length + 1).Select(i => primes[i]);
        }

        IEnumerable<int> GeneratePrimes(int lmt) {
            bool[] comps = new bool[lmt + 1];
            comps[0] = comps[1] = true;
            yield return 2; yield return 3;
            for (int j = 4; j <= lmt; j += 2) comps[j] = true;
            for (int j = 9; j <= lmt; j += 6) comps[j] = true;
            int i = 5, d = 4, rt = (int)Math.Sqrt(lmt);
            for ( ; i <= rt; i += (d = 6 - d))
                if (!comps[i]) {
                    yield return i;
                    for (int j = i * i, k = i << 1; j <= lmt; j += k)
                        comps[j] = true;
                }
            for ( ; i <= lmt; i += (d = 6 - d)) if (!comps[i]) yield return i;
        }
    }
}

C++: #include <iostream>
#include <cstdint>
#include <vector>
#include "prime_sieve.hpp"

using integer = uint32_t;
using vector = std::vector<integer>;

void print_vector(const vector& vec) {
    if (!vec.empty()) {
        auto i = vec.begin();
        std::cout << '(' << *i;
        for (++i; i != vec.end(); ++i)
            std::cout << ", " << *i;
        std::cout << ')';
    }
}

class diffs {
public:
    diffs(std::initializer_list<integer> list) : diffs_(list) {}
    diffs(const vector& vec) : diffs_(vec) {}
    void test_group(const vector&);
    size_t size() const {
        return diffs_.size();
    }
    void print(std::ostream&);
private:
    vector diffs_;
    vector first_;
    vector last_;
    integer count_ = 0;
};

void diffs::test_group(const vector& vec) {
    if (vec.size() < size() + 1)
        return;
    size_t start = vec.size() - size() - 1;
    for (size_t i = 0, j = start + 1; i < size(); ++i, ++j) {
        if (vec[j] - vec[j - 1] != diffs_[i])
            return;
    }
    vector group(vec.begin() + start, vec.end());
    if (count_ == 0)
        first_ = group;
    last_ = group;
    ++count_;
}

void diffs::print(std::ostream& out) {
    print_vector(diffs_);
    out << ": first group = ";
    print_vector(first_);
    out << ", last group = ";
    print_vector(last_);
    out << ", count = " << count_ << '\n';
}

int main() {
    const integer limit = 1000000;
    const size_t max_group_size = 4;
    prime_sieve sieve(limit);
    diffs d[] = { {2}, {1}, {2, 2}, {2, 4}, {4, 2}, {6, 4, 2} };
    vector group;
    for (integer p = 0; p < limit; ++p) {
        if (!sieve.is_prime(p))
            continue;
        if (group.size() >= max_group_size)
            group.erase(group.begin());
        group.push_back(p);
        for (auto&& diff : d) {
            diff.test_group(group);
        }
    }
    for (auto&& diff : d) {
        diff.print(std::cout);
    }
    return 0;
}