Find all the five digit primes with this property

Find all the five digit prime numbers such that the product of their digits equals some number squared multiplied by another number such as 7^2 * 5 for example.

• HAve you tried anything? – Mark Bennet Aug 18 '13 at 19:47
• Any number equals the product of a square and some number – Hagen von Eitzen Aug 18 '13 at 19:50
• oops, sorry I misread sum instead of product, the list contains $6021$ primes. How many do you have? – draks ... Aug 18 '13 at 21:15
• That's very true. At the very least, you can write something as a product of a number and one squared. – Fixed Point Aug 18 '13 at 21:16
• No that's not true – Kelly Henrehan Aug 18 '13 at 21:33

$11119,11149,11159,11177,11197,11239,11243,11261,11279,11287,11299,11329,11353,11369,11383,11393,11399,11411,11423,11437,11443,11447,11467,11471,11483,11489,11491,11497,11519,11549,11551,11579,11587,11593,11597,11621,11633,11677,11681,11689,11699,11717,11719,11743,11777,11779,11783,11789,11813,11821,11827,11831,11833,11839,11863,11867,11887,11897,11923,11927,11933,11939,11941,11953,11959,11969,11971,11981,11987,12119,12143,12149,12161,12163,12197,12211,12227,12239,12241,12251,12253,12263,12269,12277,12281,12289,12323,12329,12343,12347,12373,12377,12379,12391,12413,12421,12433,12437,12451,12457,12473,12479,12487,12491,12497,12527,12539,12541,12547,12553,12569,12577,12583,12589,12611,12613,12619,12637,12641,12647,12653,12659,12671,12689,12697,12721,12739,12743,12757,12763,12781,12791,12799,12821,12823,12829,12841,12853,12889,12893,12899,12911,12917,12919,12923,12941,12953,12959,12967,12973,12979,12983,13147,13159,13163,13177,13183,13187,13219,13229,13241,13249,13259,13267,13291,13297,13313,13327,13331,13337,13339,13367,13381,13397,13399,13411,13417,13421,13441,13451,13457,13463,13469,13477,13487,13499,13513,13523,13537,13553,13567,13577,13591,13597,13613,13619,13627,13633,13649,13669,13679,13681,13687,13691,13693,13697,13723,13729,13757,13759,13763,13781,13789,13799,13829,13831,13841,13859,13873,13877,13879,13883,13913,13921,13931,13933,13963,13967,13997,13999,14143,14149,14153,14159,14173,14177,14197,14221,14243,14249,14251,14281,14293,14321,14323,14327,14341,14347,14369,14387,14389,14411,14419,14423,14431,14437,14447,14449,14461,14479,14489,14519,14533,14537,14543,14549,14551,14557,14561,14563,14591,14593,14621,14627,14629,14633,14639,14653,14657,14669,14683,14699,14713,14717,14723,14731,14737,14741,14747,14753,14759,14767,14771,14779,14783,14797,14813,14821,14827,14831,14843,14851,14867,14869,14879,14887,14891,14897,14923,14929,14939,14947,14951,14957,14969,14983,15139,15149,15187,15193,15199,15227,15233,15241,15259,15263,15269,15277,15287,15289,15299,15313,15319,15329,15331,15349,15359,15361,15373,15377,15383,15391,15413,15427,15439,15443,15451,15461,15467,15473,15493,15497,15511,15527,15541,15551,15559,15569,15581,15583,15619,15629,15641,15643,15647,15649,15661,15667,15679,15683,15727,15733,15737,15739,15749,15767,15773,15787,15791,15797,15817,15823,15859,15877,15881,15887,15889,15913,15919,15923,15937,15959,15971,15973,15991,16127,16139,16141,16183,16187,16189,16193,16217,16223,16229,16231,16249,16253,16267,16273,16319,16333,16339,16349,16361,16363,16369,16381,16411,16417,16421,16427,16433,16447,16451,16453,16477,16481,16487,16493,16519,16529,16547,16553,16561,16567,16573,16619,16631,16633,16649,16651,16657,16661,16673,16691,16693,16699,16729,16741,16747,16759,16763,16787,16811,16823,16829,16831,16843,16871,16879,16883,16889,16921,16927,16931,16937,16943,16963,16979,16981,16987,16993,17117,17137,17159,17167,17183,17189,17191,17239,17257,17291,17293,17299,17317,17327,17333,17341,17359,17377,17383,17387,17389,17393,17417,17419,17431,17443,17449,17467,17471,17477,17483,17489,17491,17497,17519,17539,17551,17569,17573,17579,17581,17597,17599,17623,17627,17657,17659,17669,17681,17683,17713,17729,17737,17747,17749,17761,17783,17789,17791,17827,17837,17839,17851,17863,17881,17891,17911,17921,17923,17929,17939,17957,17959,17971,17977,17981,17987,17989,18119,18121,18127,18131,18133,18143,18149,18169,18181,18191,18199,18211,18217,18223,18229,18233,18251,18253,18257,18269,18287,18289,18311,18313,18329,18341,18353,18367,18371,18379,18397,18413,18427,18433,18439,18443,18451,18457,18461,18481,18493,18517,18521,18523,18539,18541,18553,18583,18587,18593,18617,18637,18661,18671,18679,18691,18713,18719,18731,18743,18749,18757,18773,18787,18793,18797,18839,18859,18869,18899,18911,18913,18917,18919,18947,18959,18973,18979,19121,19139,19141,19157,19163,19181,19183,19211,19213,19219,19231,19237,19249,19259,19267,19273,19289,19319,19333,19373,19379,19381,19387,19391,19417,19421,19423,19427,19429,19433,19441,19447,19457,19463,19469,19471,19477,19483,19489,19531,19541,19543,19553,19559,19571,19577,19583,19597,19661,19681,19687,19697,19699,19717,19727,19739,19751,19753,19759,19763,19777,19793,19813,19819,19841,19843,19853,19861,19867,19889,19891,19913,19919,19927,19937,19949,19961,19963,19973,19979,19991,19993,19997,21121,21139,21143,21149,21163,21169,21179,21187,21191,21193,21211,21221,21227,21247,21269,21277,21283,21313,21319,21323,21341,21347,21377,21379,21383,21391,21397,21419,21433,21467,21481,21487,21491,21493,21499,21521,21523,21529,21557,21559,21563,21569,21577,21587,21589,21599,21611,21613,21617,21647,21649,21661,21673,21683,21727,21737,21739,21757,21767,21773,21787,21799,21817,21821,21839,21841,21851,21859,21863,21871,21881,21893,21911,21929,21937,21943,21961,21977,21991,21997,22111,22123,22129,22133,22147,22153,22157,22159,22171,22189,22193,22229,22247,22259,22271,22273,22277,22279,22283,22291,22343,22349,22367,22369,22381,22391,22397,22433,22441,22447,22453,22469,22481,22483,22511,22531,22541,22543,22549,22567,22571,2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