/* Select the required print out. Digit: 0 for Prime Numbers until max, with info on related k-tuples. 1 for Prime Numbers Twin Pairs until max. 2 for Prime Numbers Cousin Pairs until max. 3 for Prime Numbers Sexy Pairs until max. 4 for Prime Numbers Triplets until max. 5 for Prime Numbers Quadruplets until max. 6 for Prime Numbers Quintuplets until max. 7 for Prime Numbers Sextuplets until max. 8 for Sexy Prime Numbers Triplets until max. 9 for Sexy Prime Numbers Quadruplets until max. An integer from 10 to max for k-tuples on the specified prime number. In case of input error the default selection will be used max and defaultInputValue are defined at begin of the program and can be changed if needed. Time limit problems on SoloLearn. */ import java.util.*; import java.util.Scanner; public class NumeriPrimi implements PrimeCostants { private static Scanner myInput; public static void main(String[] args) { Map primeList = new TreeMap(); int max = 1000; int defaultInputValue = 0; // Default value from Input Selection createPrimeList (max+20,primeList); updatePrimeList (primeList); int selection = fetchInputRequest(defaultInputValue, max); switch (selection) { case 0: printPrimeList (primeList, max); break; case 1: printKTuplesList (primeList, max, 2, "Twin"); // Print Prime Twin Pairs break; case 2: printKTuplesList (primeList, max, 4, "Cousin"); // Print Prime Cousin Pairs break; case 3: printKTuplesList (primeList, max, 6, "Sexy"); // Print Prime Sexy Pairs break; case 4: printK2TuplesList (primeList, max, 2, 6, "Number"); // Print Prime Triplets break; case 5: printKTuplesList (primeList, max, 2, 6, 8, "Number"); // Print Prime Quadruplets break; case 6: printK2TuplesList (primeList, max, 2, 6, 8, 12, "Number"); // Print Prime Quintuplets break; case 7: printKTuplesList (primeList, max, 4, 6, 10, 12, 16, "Number"); // Print Prime Sextuplets break; case 8: printKTuplesList (primeList, max, 6, 12, "Sexy"); // Print Sexy Prime Triplets break; case 9: printKTuplesList (primeList, max, 6, 12, 18, "Sexy"); // Print Sexy Prime Quadruplets break; default: printSinglePrime (primeList, max, selection); // Print k-tuples for selected number break; } } // Create an Hash List with Prime numbers as Key public static void createPrimeList(int maxCheck, Map primeList) { primeList.put(2,0); for (int i = 3; i <= maxCheck; i+= 2) { int j = (int) Math.floor(Math.sqrt(i)); boolean primenumb = true; for (Integer key : primeList.keySet()) { if (key > j) break; if (i % key == 0) { primenumb = false; break; } } if (primenumb == true) { primeList.put(i,0); } } } // Add to the Prime list the info on closer prime numbers. public static void updatePrimeList(Map primeList) { for (Integer key : primeList.keySet()) { int value = 512; // Math.pow(2,9) for (int i=1; i<10; i++) { if (primeList.containsKey(key-2*i)) value += Math.pow(2.0, 9-i); if (primeList.containsKey(key+2*i)) value += Math.pow(2.0, i+9); } primeList.put(key, value); } } // Print List of Prime with the indication on the numbers of related k-tuples public static void printPrimeList(Map primeList, int max) { int index, twins, cousins, sexys, triplets, quadruplets, quintuplet, sextuplet, sextrip, sexquad; index = 0; System.out.println("\n" + "List of Prime Numbers until " + max + " with info on related k-tuples"); System.out.printf("%n%5s %7s %2s %2s %2s %2s %2s %2s %2s %2s %2s %n", "Index", "Prime", "T","C", "S", "P", "P", "P", "P", "S", "S"); System.out.printf("%5s %7s %2s %2s %2s %2s %2s %2s %2s %2s %2s %n", " ", "Numbers", "w","o", "e", "3", "4", "5", "6", "3", "4"); System.out.printf("%5s %7s %2s %2s %2s %2s %2s %2s %2s %2s %2s %n", "-----", "-------", "-", "-", "-", "-", "-", "-", "-", "-", "-"); for (Map.Entry entry : primeList.entrySet()) { if (entry.getKey() > max) break; twins = 0; cousins = 0; sexys = 0; triplets = 0; quadruplets = 0; quintuplet = 0; sextuplet = 0; sextrip = 0; sexquad = 0; if (L02==(L02&entry.getValue())) twins++; if (R02==(R02&entry.getValue())) twins++; if (L04==(L04&entry.getValue())) cousins++; if (R04==(R04&entry.getValue())) cousins++; if (L06==(L06&entry.getValue())) sexys++; if (R06==(R06&entry.getValue())) sexys++; if ((P31==(P31&entry.getValue())) || (P32==(P32&entry.getValue()))) triplets++; if ((P33==(P33&entry.getValue())) || (P34==(P34&entry.getValue()))) triplets++; if ((P35==(P35&entry.getValue())) || (P36==(P36&entry.getValue()))) triplets++; if ((P41==(P41&entry.getValue())) || (P42==(P42&entry.getValue()))) quadruplets++; if ((P43==(P43&entry.getValue())) || (P44==(P44&entry.getValue()))) quadruplets++; if ((P51==(P51&entry.getValue())) || (P52==(P52&entry.getValue()))) quintuplet++; if ((P53==(P53&entry.getValue())) || (P54==(P54&entry.getValue()))) quintuplet++; if ((P55==(P55&entry.getValue())) || (P56==(P56&entry.getValue()))) quintuplet++; if ((P57==(P57&entry.getValue())) || (P58==(P58&entry.getValue()))) quintuplet++; if ((P59==(P59&entry.getValue())) || (P50==(P50&entry.getValue()))) quintuplet++; if ((P61==(P61&entry.getValue())) || (P62==(P62&entry.getValue()))) sextuplet++; if ((P63==(P63&entry.getValue())) || (P64==(P64&entry.getValue()))) sextuplet++; if ((P65==(P65&entry.getValue())) || (P66==(P66&entry.getValue()))) sextuplet++; if (S31==(S31&entry.getValue())) sextrip++; if (S32==(S32&entry.getValue())) sextrip++; if (S33==(S33&entry.getValue())) sextrip++; if (S41==(S41&entry.getValue())) sexquad++; if (S42==(S42&entry.getValue())) sexquad++; if (S43==(S43&entry.getValue())) sexquad++; if (S44==(S44&entry.getValue())) sexquad++; System.out.printf("%5d %7d %2s %2s %2s %2s %2s %2s %2s %2s %2s %n", ++index, entry.getKey(), twins==0?"":twins, cousins==0?"":cousins, sexys==0?"":sexys, triplets==0?"":triplets, quadruplets==0?"":quadruplets, quintuplet==0?"":quintuplet, sextuplet==0?"":sextuplet, sextrip==0?"":sextrip, sexquad==0?"":sexquad); if (index % 5 == 0) { System.out.printf("%5s %7s %2s %2s %2s %2s %2s %2s %2s %2s %2s %n", "-----", "-------", "-", "-", "-", "-", "-", "-", "-", "-", "-"); } } } // print for a single Number all prime info public static void printSinglePrime(Map primeList, int max, int prime) { if(prime > max){ System.out.println("\n" + prime + " is greater than " + max + "." + "\n" + "Use a value less than " + max + " or change the max value in the code."); return; } if(!primeList.containsKey(prime)){ System.out.println("\n" + prime + " is not a Prime Number." + "\n" + "Try again" + "\n"); return; } int value = primeList.get(prime); System.out.println("\n" + "List of all k-tuples involving the Prime Number " + prime); System.out.println("\n" + "\n" + "Prime Twin pairs involving " + prime + ":"); if (L02==(L02&value)) System.out.println("[" + (prime-2) + ", " + (prime) + "]"); if (R02==(R02&value)) System.out.println("[" + (prime) + ", " + (prime+2) + "]"); System.out.println("\n" + "\n" + "Prime Cousin pairs involving " + prime + ":"); if (L04==(L04&value)) System.out.println("[" + (prime-4) + ", " + (prime) + "]"); if (R04==(R04&value)) System.out.println("[" + (prime) + ", " + (prime+4) + "]"); System.out.println("\n" + "\n" + "Prime Sexy pairs involving " + prime + ":"); if (L06==(L06&value)) System.out.println("[" + (prime-6) + ", " + (prime) + "]"); if (R06==(R06&value)) System.out.println("[" + (prime) + ", " + (prime+6) + "]"); System.out.println("\n" + "\n" + "Prime Number Triplets involving " + prime + ":"); if (P36==(P36&value)) System.out.println("[" + (prime-6) + ", " + (prime-2) + ", " + (prime) + "]"); if (P35==(P35&value)) System.out.println("[" + (prime-6) + ", " + (prime-4) + ", " + (prime) + "]"); if (P34==(P34&value)) System.out.println("[" + (prime-4) + ", " + (prime) + ", " + (prime+2) + "]"); if (P33==(P33&value)) System.out.println("[" + (prime-2) + ", " + (prime) + ", " + (prime+4) + "]"); if (P32==(P32&value)) System.out.println("[" + (prime) + ", " + (prime+4) + ", " + (prime+6) + "]"); if (P31==(P31&value)) System.out.println("[" + (prime) + ", " + (prime+2) + ", " + (prime+6) + "]"); System.out.println("\n" + "\n" + "Prime Number Quadruplets involving " + prime + ":"); if (P44==(P44&value)) System.out.println("[" + (prime-8) + ", " + (prime-6) + ", " + (prime-2) + ", " + (prime) + "]"); if (P43==(P43&value)) System.out.println("[" + (prime-6) + ", " + (prime-4) + ", " + (prime) + ", " + (prime+2) + "]"); if (P42==(P42&value)) System.out.println("[" + (prime-2) + ", " + (prime) + ", " + (prime+4) + ", " + (prime+6) + "]"); if (P41==(P41&value)) System.out.println("[" + (prime) + ", " + (prime+2) + ", " + (prime+6) + ", " + (prime+8) + "]"); System.out.println("\n" + "\n" + "Prime Number Quintuplets involving " + prime + ":"); if (P50==(P50&value)) System.out.println("[" + (prime-12) + ", " + (prime-8) + ", " + (prime-6) + ", " + (prime-2) + ", " + (prime) + "]"); if (P59==(P59&value)) System.out.println("[" + (prime-12) + ", " + (prime-10) + ", " + (prime-6) + ", " + (prime-4) + ", " + (prime) + "]"); if (P58==(P58&value)) System.out.println("[" + (prime-10) + ", " + (prime-6) + ", " + (prime-4) + ", " + (prime) + ", " + (prime+2) + "]"); if (P57==(P57&value)) System.out.println("[" + (prime-8) + ", " + (prime-6) + ", " + (prime-2) + ", " + (prime) + ", " + (prime+4) + "]"); if (P56==(P56&value)) System.out.println("[" + (prime-6) + ", " + (prime-2) + ", " + (prime) + ", " + (prime+4) + ", " + (prime+6) + "]"); if (P55==(P55&value)) System.out.println("[" + (prime-6) + ", " + (prime-4) + ", " + (prime) + ", " + (prime+2) + ", " + (prime+6) + "]"); if (P54==(P54&value)) System.out.println("[" + (prime-4) + ", " + (prime) + ", " + (prime+2) + ", " + (prime+6) + ", " + (prime+8) + "]"); if (P53==(P53&value)) System.out.println("[" + (prime-2) + ", " + (prime) + ", " + (prime+4) + ", " + (prime+6) + ", " + (prime+10) + "]"); if (P52==(P52&value)) System.out.println("[" + (prime) + ", " + (prime+4) + ", " + (prime+6) + ", " + (prime+10) + ", " + (prime+12) + "]"); if (P51==(P51&value)) System.out.println("[" + (prime) + ", " + (prime+2) + ", " + (prime+6) + ", " + (prime+8) + ", " + (prime+12) + "]"); System.out.println("\n" + "\n" + "Prime Number Sextuplets involving " + prime + ":"); if (P66==(P66&value)) System.out.println("[" + (prime-16) + ", " + (prime-12) + ", " + (prime-10) + ", " + (prime-6) + ", " + (prime-4) + ", " + (prime) + "]"); if (P65==(P65&value)) System.out.println("[" + (prime-12) + ", " + (prime-8) + ", " + (prime-6) + ", " + (prime-2) + ", " + (prime) + ", " + (prime+4) + "]"); if (P64==(P64&value)) System.out.println("[" + (prime-10) + ", " + (prime-6) + ", " + (prime-4) + ", " + (prime) + ", " + (prime+2) + ", " + (prime+6) + "]"); if (P63==(P63&value)) System.out.println("[" + (prime-6) + ", " + (prime-2) + ", " + (prime) + ", " + (prime+4) + ", " + (prime+6) + ", " + (prime+10) + "]"); if (P62==(P62&value)) System.out.println("[" + (prime-4) + ", " + (prime) + ", " + (prime+2) + ", " + (prime+6) + ", " + (prime+8) + ", " + (prime+12) + "]"); if (P61==(P61&value)) System.out.println("[" + (prime) + ", " + (prime+4) + ", " + (prime+6) + ", " + (prime+10) + ", " + (prime+12) + ", " + (prime+16) + "]"); System.out.println("\n" + "\n" + "Sexy Prime Triplets involving " + prime + ":"); if (S33==(S33&value)) System.out.println("[" + (prime-12) + ", " + (prime-6) + ", " + (prime) + "]"); if (S32==(S32&value)) System.out.println("[" + (prime-6) + ", " + (prime) + ", " + (prime+6) + "]"); if (S31==(S31&value)) System.out.println("[" + (prime) + ", " + (prime+6) + ", " + (prime+12) + "]"); System.out.println("\n" + "\n" + "Sexy Prime Quadruplets involving " + prime + ":"); if (S44==(S44&value)) System.out.println("[" + (prime-18) + ", " + (prime-12) + ", " + (prime-6) + ", " + (prime) + "]"); if (S43==(S43&value)) System.out.println("[" + (prime-12) + ", " + (prime-6) + ", " + (prime) + ", " + (prime+6) + "]"); if (S42==(S42&value)) System.out.println("[" + (prime-6) + ", " + (prime) + ", " + (prime+6) + ", " + (prime+12) + "]"); if (S41==(S41&value)) System.out.println("[" + (prime) + ", " + (prime+6) + ", " + (prime+12) + ", " + (prime+18) + "]"); } // Print Douplets public static void printKTuplesList(Map primeList, int max, int step1, String text) { int filter = (int) (512 * Math.pow(2, step1/2)); int index; index = 0; System.out.println("\n" + "\n" + "List of Prime " + text + " Numbers until " + max); System.out.printf("%n%8s %15s %-15s %n", "Index", "Prime", text); System.out.printf("%8s %15s %-15s %n", " ", "Numbers", "primes"); System.out.printf("%8s %15s %-15s %n", "-----", "------------", "------------"); for (Map.Entry entry : primeList.entrySet()) { if (entry.getKey() > max) break; if (filter==(filter&entry.getValue())) { System.out.printf("%8d %15d %-15s %n", ++index, entry.getKey(), entry.getKey()+step1); if (index % 5 == 0) { System.out.printf("%8s %15s %-15s %n", "-----", "------------", "------------"); } } } } // Print Triplets public static void printKTuplesList(Map primeList, int max, int step1, int step2, String text) { int filter = (int) (512 * Math.pow(2, step1/2) + (512 * Math.pow(2, step2/2))); int index; index = 0; System.out.println("\n" + "\n" + "List of Prime " + text + " Triplets until " + max); System.out.printf("%n %7s %10s %10s %-10s %n", "Index", "Prime", text, "Tripletes"); System.out.printf("%8s %10s %10s %10s %n", "-----", "----------", "----------", "----------"); for (Map.Entry entry : primeList.entrySet()) { if (entry.getKey() > max) break; if (filter==(filter&entry.getValue())) { System.out.printf("%8d %10d %10s %10s %n", ++index, entry.getKey(), entry.getKey()+step1, entry.getKey()+step2); if (index % 5 == 0) { System.out.printf("%8s %10s %10s %10s %n", "-----", "----------", "----------", "----------"); } } } } // Print Quadruplets public static void printKTuplesList(Map primeList, int max, int step1, int step2, int step3, String text) { int filter = (int) (512 * Math.pow(2, step1/2) + (512 * Math.pow(2, step2/2)) + (512 * Math.pow(2, step3/2))); int index; index = 0; System.out.println("\n" + "\n" + "List of Prime " + text + " Quadruplets until " + max); System.out.printf("%n %-5s %7s %7s %-7s %n", "Index", "Prime", text, "Quadrupletes"); System.out.printf("%6s %7s %7s %7s %7s %n", "------", "-------", "-------", "-------", "-------"); for (Map.Entry entry : primeList.entrySet()) { if (entry.getKey() > max) break; if (filter==(filter&entry.getValue())) { System.out.printf("%6d %7d %-7s %7s %-7s %n", ++index, entry.getKey(), entry.getKey()+step1, entry.getKey()+step2, entry.getKey()+step3); if (index % 5 == 0) { System.out.printf("%6s %7s %7s %7s %7s %n", "------", "-------", "-------", "-------", "-------"); } } } } // Print Sextuplets public static void printKTuplesList(Map primeList, int max, int step1, int step2, int step3, int step4, int step5, String text) { int filter = (int) (512 * Math.pow(2, step1/2) + (512 * Math.pow(2, step2/2)) + (512 * Math.pow(2, step3/2)) + (512 * Math.pow(2, step4/2)) + (512 * Math.pow(2, step5/2))); int index; index = 0; System.out.println("\n" + "\n" + "List of Prime " + text + " Sextuplets until " + max); System.out.printf("%n %5s %6s %6s %-15s %n", "Index", "Prime", text, "Sextupletes"); System.out.printf("%6s %25s %n", "------", " ------------------------"); for (Map.Entry entry : primeList.entrySet()) { if (entry.getKey() > max) break; if (filter==(filter&entry.getValue())) { System.out.printf("%6d %1s", ++index, " "); System.out.println("[" + (entry.getKey()) + ", " + (entry.getKey()+step1) + ", " + (entry.getKey()+step2) + ", " + (entry.getKey()+step3) + ", " + (entry.getKey()+step4) + ", " + (entry.getKey()+step5) + "]"); if (index % 5 == 0) { System.out.printf("%6s %25s %n", "------", " ------------------------"); } } } } // Print Triplets Double public static void printK2TuplesList(Map primeList, int max, int step1, int step2, String text) { int filter1 = (int) (512 * Math.pow(2, step1/2) + (512 * Math.pow(2, step2/2))); int filter2 = (int) (512 * Math.pow(2, (step1 + 2)/2) + (512 * Math.pow(2, step2/2))); int index; index = 0; System.out.println("\n" + "\n" + "List of Prime " + text + " Triplets until " + max); System.out.printf("%n %7s %10s %10s %-10s %n", "Index", "Prime", text, "Tripletes"); System.out.printf("%8s %10s %10s %10s %n", "-----", "----------", "----------", "----------"); for (Map.Entry entry : primeList.entrySet()) { if (entry.getKey() > max) break; if (filter1==(filter1&entry.getValue())) { System.out.printf("%8d %10d %-10s %-10s %n", ++index, entry.getKey(), entry.getKey()+step1, entry.getKey()+step2); if (index % 5 == 0) { System.out.printf("%8s %10s %10s %10s %n", "-----", "----------", "----------", "----------"); } } if (filter2==(filter2&entry.getValue())) { System.out.printf("%8d %10d %10s %-10s %n", ++index, entry.getKey(), entry.getKey()+step1+2, entry.getKey()+step2); if (index % 5 == 0) { System.out.printf("%8s %10s %10s %10s %n", "-----", "----------", "----------", "----------"); } } } } // Print Quintuplets Double public static void printK2TuplesList(Map primeList, int max, int step1, int step2, int step3, int step4, String text) { int filter1 = (int) (512 * Math.pow(2, step1/2) + (512 * Math.pow(2, step2/2)) + (512 * Math.pow(2, step3/2)) + (512 * Math.pow(2, step4/2))); int filter2 = (int) (512 * Math.pow(2, (step1 + 2)/2) + (512 * Math.pow(2, step2/2)) + (512 * Math.pow(2, (step3+2)/2)) + (512 * Math.pow(2, step4/2))); int index; index = 0; System.out.println("\n" + "\n" + "List of Prime " + text + " Quintuplets until " + max); System.out.printf("%n %5s %6s %6s %-15s %n", "Index", "Prime", text, "Quintupletes"); System.out.printf("%6s %25s %n", "------", " ------------------------"); for (Map.Entry entry : primeList.entrySet()) { if (entry.getKey() > max) break; if (filter1==(filter1&entry.getValue())) { System.out.printf("%6d %1s", ++index, " "); System.out.println("[" + (entry.getKey()) + ", " + (entry.getKey()+step1) + ", " + (entry.getKey()+step2) + ", " + (entry.getKey()+step3) + ", " + (entry.getKey()+step4) + "]"); if (index % 5 == 0) { System.out.printf("%6s %25s %n", "------", " ------------------------"); } } if (filter2==(filter2&entry.getValue())) { System.out.printf("%6d %1s", ++index, " "); System.out.println("[" + (entry.getKey()) + ", " + (entry.getKey()+step1+2) + ", " + (entry.getKey()+step2) + ", " + (entry.getKey()+step3+2) + ", " + (entry.getKey()+step4) + "]"); if (index % 5 == 0) { System.out.printf("%6s %25s %n", "------", " ------------------------"); } } } } @SuppressWarnings("finally") static int fetchInputRequest(int defaultValue, int max) { int requestValue = defaultValue; System.out.println("\n" + "Select the required print out. Digit:"); System.out.println("0 for Prime Numbers until " + max + ", plus info"); System.out.println("1 for Prime Numbers Twin Pairs (Tw)."); System.out.println("2 for Prime Numbers Cousin Pairs (Co)."); System.out.println("3 for Prime Numbers Sexy Pairs (Se)."); System.out.println("4 for Prime Numbers Triplets (P3)."); System.out.println("5 for Prime Numbers Quadruplets (P4)."); System.out.println("6 for Prime Numbers Quintuplets (P5)."); System.out.println("7 for Prime Numbers Sextuplets (P6)."); System.out.println("8 for Sexy Prime Numbers Triplets (S3)."); System.out.println("9 for Sexy Prime Numbers Quadruplets (S4)"); System.out.println("An integer from 10 to " + max + " for k-tuples on the specified prime number."); try { myInput = new Scanner(System.in); requestValue = myInput.nextInt(); System.out.println("\n" + "The input value is: " + requestValue); } catch (Exception e) { System.out.println("\n" + "Input not valid, used default value: " + defaultValue); } finally { return requestValue; } } } interface PrimeCostants { // Prime Numbers lower than P final int L18 = 1; // 2^0 Distant 18 Left (P-18) final int L16 = 2; // 2^1 Distant 16 Left (P-16) // final int L14 = 4; // 2^2 Distant 14 Left (P-14) final int L12 = 8; // 2^3 Distant 12 Left (P-12) final int L10 = 16; // 2^4 Distant 10 Left (P-10) final int L08 = 32; // 2^5 Distant 8 Left (P- 8) final int L06 = 64; // 2^6 Distant 6 Left (P- 6) Sexy Prime Number final int L04 = 128; // 2^7 Distant 4 Left (P- 4) Cousin Prime Number final int L02 = 256; // 2^8 Distant 2 Left (P- 2) Twin Prime Number // Prime Numbers higher than P final int R02 = 1024; // 2^10 Distant 2 Right (P+ 2) Twin Prime Number final int R04 = 2048; // 2^11 Distant 4 Right (P+ 4) Cousin Prime Number final int R06 = 4096; // 2^12 Distant 6 Right (P+ 6) Sexy Prime Number final int R08 = 8192; // 2^13 Distant 8 Left (P+ 8) final int R10 = 16384; // 2^14 Distant 10 Left (P+10) final int R12 = 32768; // 2^15 Distant 12 Left (P+12) // final int R14 = 65536; // 2^16 Distant 14 Left (P+14) final int R16 = 131072; // 2^17 Distant 16 Left (P+16) final int R18 = 262144; // 2^18 Distant 18 Left (P+18) // Filter for Prime Triplets: (0, 2, 6), (0, 4, 6) final int P31 = R02 + R06; // ( P ,(P+ 2),(P+ 6)) final int P32 = R04 + R06; // ( P ,(P+ 4),(P+ 6)) final int P33 = L02 + R04; // ((P- 2), P ,(P+ 4)) final int P34 = L04 + R02; // ((P- 4), P ,(P+ 2)) final int P35 = L06 + L04; // ((P- 6),(P- 4), P ) final int P36 = L06 + L02; // ((P- 6),(P- 2), P ) // Filter for Prime Quadruplets: (0, 2, 6, 8) final int P41 = R02 + R06 + R08; // ( P ,(P+ 2),(P+ 6),(P+ 8)) final int P42 = L02 + R04 + R06; // ((P- 2), P ,(P+ 4),(P+ 6)) final int P43 = L06 + L04 + R02; // ((P- 6),(P- 4), P ,(P+ 2)) final int P44 = L08 + L06 + L02; // ((P- 8),(P- 6),(P- 2), P ) // Filter for Prime Quintuplets: (0, 2, 6, 8, 12), (0, 4, 6, 10, 12) final int P51 = R02 + R06 + R08 + R12; // ( P ,(P+ 2),(P+ 6),(P+ 8),(P+12)) final int P52 = R04 + R06 + R10 + R12; // ( P ,(P+ 4),(P+ 6),(P+10),(P+12)) final int P53 = L02 + R04 + R06 + R10; // ((P- 2), P ,(P+ 4),(P+ 6),(P+10)) final int P54 = L04 + R02 + R06 + R08; // ((P- 4), P ,(P+ 2),(P+ 6),(P+ 8)) final int P55 = L06 + L04 + R02 + R06; // ((P- 6),(P- 4), P ,(P+ 2),(P+ 6)) final int P56 = L06 + L02 + R04 + R06; // ((P- 6),(P- 2), P ,(P+ 4),(P+ 6)) final int P57 = L08 + L06 + L02 + R04; // ((P- 8),(P- 6),(P- 2), P ,(P+ 4)) final int P58 = L10 + L06 + L04 + R02; // ((P-10),(P- 6),(P- 4), P ,(P+ 2)) final int P59 = L12 + L10 + L06 + L04; // ((P-12),(P-10),(P- 6),(P- 4), P ) final int P50 = L12 + L08 + L06 + L02; // ((P-12),(P- 8),(P- 6),(P- 2), P ) // Filter for Prime Sextuplets: (0, 4, 6, 10, 12, 16) final int P61 = R04 + R06 + R10 + R12 + R16; // ( P ,(P+ 4),(P+ 6),(P+10),(P+12),(P+16)) final int P62 = L04 + R02 + R06 + R08 + R12; // ((P- 4), P ,(P+ 2),(P+ 6),(P+ 8),(P+12)) final int P63 = L06 + L02 + R04 + R06 + R10; // ((P- 6),(P- 2), P ,(P+ 4),(P+ 6),(P+10)) final int P64 = L10 + L06 + L04 + R02 + R06; // ((P-10),(P- 6),(P- 4), P ,(P+ 2),(P+ 6)) final int P65 = L12 + L08 + L06 + L02 + R04; // ((P-12),(P- 8),(P- 6),(P- 2), P ,(P+ 4)) final int P66 = L16 + L12 + L10 + L06 + L04; // ((P-16),(P-12),(P-10),(P- 6),(P- 4), P ) // Filter for Sexy Prime Triplets: (0, 6, 12) final int S31 = R06 + R12; // ( P ,(P+ 6),(P+12)) final int S32 = L06 + R06; // ((P- 6), P ,(P+ 6)) final int S33 = L12 + L06; // ((P-12),(P- 6), P ) // Filter for Sexy Prime Quadruplets: (0, 6, 12, 18) final int S41 = R06 + R12 + R18; // ( P ,(P+ 6),(P+12),(P+18)) final int S42 = L06 + R06 + R12; // ((P- 6), P ,(P+ 6),(P+12)) final int S43 = L12 + L06 + R06; // ((P-12),(P- 6), P ,(P+ 6)) final int S44 = L18 + L12 + L06; // ((P-18),(P-12),(P- 6), P ) }

Prime k-tuples