Comments on: Google Treasure Hunt 2008 Puzzle 4

By: Vaibhav Bansal

Vaibhav Bansal — Fri, 06 Apr 2012 12:14:19 +0000

The solution above is implemented in java and the output is :
smallest prime No : 7830239
7 prime nos : [1118563, 1118567, 1118569, 1118599, 1118629, 1118653, 1118659]
17 prime nos : [460463, 460477, 460531, 460543, 460561, 460571, 460589, 460609, 460619, 460627, 460633, 460637, 460643, 460657, 460673, 460697, 460709]
41 prime nos : [190759, 190763, 190769, 190783, 190787, 190793, 190807, 190811, 190823, 190829, 190837, 190843, 190871, 190889, 190891, 190901, 190909, 190913, 190921, 190979, 190997, 191021, 191027, 191033, 191039, 191047, 191057, 191071, 191089, 191099, 191119, 191123, 191137, 191141, 191143, 191161, 191173, 191189, 191227, 191231, 191237]
541 prime nos : [11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967, 13997, 13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 14083, 14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401, 15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569, 15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, 15661, 15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, 15761, 15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, 15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959, 15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, 16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187, 16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301, 16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421, 16427, 16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529, 16547, 16553, 16561, 16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, 16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883, 16889, 16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981, 16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, 17093]

By: Vaibhav Bansal

Vaibhav Bansal — Fri, 06 Apr 2012 12:13:30 +0000

package com.algorithm;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class Prime {

public static boolean isNumberPrime(long number) {

for (long i = 3l; i <= Math.sqrt(number); i += 2) {
if(number % i == 0) {
return false;
}
}
return true;
}

public static void main(String[] args) {

List primeNoList = new ArrayList();

primeNoList.add(1);
primeNoList.add(2);
for (int i=3; i<=8000000; i+=2) {
if(isNumberPrime(i)) {
primeNoList.add(i);
}
}

Map sumConsecutivePrimeNos0 = sumConsecutivePrimeNos(7, primeNoList);
Map sumConsecutivePrimeNos1 = sumConsecutivePrimeNos(17, primeNoList);
Map sumConsecutivePrimeNos2 = sumConsecutivePrimeNos(41, primeNoList);
Map sumConsecutivePrimeNos3 = sumConsecutivePrimeNos(541, primeNoList);

for (Integer smallestPrimeNo : primeNoList) {
if (sumConsecutivePrimeNos0.containsKey(smallestPrimeNo) &&
sumConsecutivePrimeNos1.containsKey(smallestPrimeNo) &&
sumConsecutivePrimeNos2.containsKey(smallestPrimeNo) &&
sumConsecutivePrimeNos3.containsKey(smallestPrimeNo)) {
System.out.println(“smallest prime No : ” + smallestPrimeNo);
System.out.println(“7 consecutive prime nos : ” + sumConsecutivePrimeNos0.get(smallestPrimeNo));
System.out.println(“17 consecutive prime nos : ” + sumConsecutivePrimeNos1.get(smallestPrimeNo));
System.out.println(“41 consecutive prime nos : ” + sumConsecutivePrimeNos2.get(smallestPrimeNo));
System.out.println(“541 consecutive prime nos : ” + sumConsecutivePrimeNos3.get(smallestPrimeNo));
break;
}
}
}

private static Map sumConsecutivePrimeNos(int count, List primeNoList) {

Map map = new HashMap();

for (int i = 0; i < primeNoList.size() – count; i++) {
List consecutiveList = primeNoList.subList(i, i + count);
int sum = 0;
for (int primeNo : consecutiveList) {
sum += primeNo;
}
if (sum > primeNoList.get(primeNoList.size() – 1)) {
break;
}
if (isNumberPrime(sum)) {
map.put(sum, consecutiveList);
}
}
return map;
}
}

By: FalconNL

FalconNL — Thu, 16 Apr 2009 22:23:08 +0000

In Haskell: [sourcecode lang='css'] import Data.List import Data.Numbers.Primes main = print $ test [541,41,17,7,1] consecutivePrimes n = map (sum . take n) $ tails primes test = head . foldl1 (\a b -> filter (\x -> elem x $ takeWhile (<= x) b) a) . map consecutivePrimes[/sourcecode]

By: jcs

jcs — Thu, 16 Apr 2009 19:45:22 +0000

Here is a solution that makes no assumptions about the size of the solution and does not compute unnecessary sums. The primes module provides a stream (as in SICP) of primes and the primitive prime?; push, pop, and dotimes are Scheme implementations of the like-named Common Lisp macros.

(use-modules (private primes)) ;for stream-of-primes, prime?


;;; Queue object that holds n consecutive primes and sums them

(define make-summing-queue

  (lambda (n)

    (let ((front '()) (back '()) (primes stream-of-primes))

      (define popq    ;just throw away the head of queue

        (lambda ()

          (unless (pop front)

            (set! front (reverse back))

            (set! back '())

            (pop front))))

      (define popp    ;return the next prime

        (lambda ()

          (let ((p (str-car primes)))

            (set! primes (str-cdr primes))

            p)))

      (dotimes (i n)

        (push (popp) back))

      (lambda (cmd)

        (case cmd

          ((next) (push (popp) back) (popq))   ;shift sum

          ((fb) (format #t "front: ~s, back: ~s\n" front back))

          ((show) (princ (append front (reverse back))))

          ((sum) (apply + (append front back))))))))
;;; Find sums of primes
(define queues (list (make-summing-queue 541)

                     (make-summing-queue 41)

                     (make-summing-queue 17)

                     (make-summing-queue 7)))
(define run

  (lambda (queues)

    (let ((first (car queues)))

      (while (not (prime? (first 'sum)))

        (first 'next))

      (let iter ((goal (first 'sum)) (rest (cdr queues)))

        (cond ((null? rest) (first 'sum))

              ((= goal ((car rest) 'sum)) (iter goal (cdr rest)))

              ((< goal ((car rest) 'sum)) (first 'next) (run queues))

              (else ((car rest) 'next) (iter goal rest)))))))

;; (for-each (lambda (q) (q 'show)) queues) ;; to see lists of primes