 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Semiprime Names (Posted on 2010-12-06) Six is a semiprime (the product of two primes). Its name, written in English, has 3 letters and 3 is one of the two primes that produce 6.

What 2-digit semiprime is like that?

What is the smallest such 3-digit semiprime?

What is the smallest such 4-digit semiprime?

Consider two cases for each:

• Use the word "and" in all numbers such as "one-hundred and one".
• Don't use the word "and" in those numbers.

In any event, don't use locutions such as "nineteen hundred"; rather, use "one thousand nine hundred" for this example.

 Submitted by Charlie No Rating Solution: (Hide) The respective sets of numbers that meet the criteria, their names and the prime factors for such numbers under 10,000 are (the first prime factor shown is the number of letters in the name): ``` 6 SIX 3 2 33 THIRTY-THREE 11 3 253 TWO HUNDRED AND FIFTY-THREE 23 11 299 TWO HUNDRED AND NINETY-NINE 23 13 667 SIX HUNDRED AND SIXTY-SEVEN 23 29 713 SEVEN HUNDRED AND THIRTEEN 23 31 851 EIGHT HUNDRED AND FIFTY-ONE 23 37 901 NINE HUNDRED AND ONE 17 53 1007 ONE THOUSAND AND SEVEN 19 53 1081 ONE THOUSAND AND EIGHTY-ONE 23 47 3293 THREE THOUSAND TWO HUNDRED AND NINETY-THREE 37 89 3589 THREE THOUSAND FIVE HUNDRED AND EIGHTY-NINE 37 97 4009 FOUR THOUSAND AND NINE 19 211 4309 FOUR THOUSAND THREE HUNDRED AND NINE 31 139 4847 FOUR THOUSAND EIGHT HUNDRED AND FORTY-SEVEN 37 131 5587 FIVE THOUSAND FIVE HUNDRED AND EIGHTY-SEVEN 37 151 5611 FIVE THOUSAND SIX HUNDRED AND ELEVEN 31 181 6001 SIX THOUSAND AND ONE 17 353 6049 SIX THOUSAND AND FORTY-NINE 23 263 7409 SEVEN THOUSAND FOUR HUNDRED AND NINE 31 239 6 SIX 3 2 33 THIRTY-THREE 11 3 551 FIVE HUNDRED FIFTY-ONE 19 29 1147 ONE THOUSAND ONE HUNDRED FORTY-SEVEN 31 37 1271 ONE THOUSAND TWO HUNDRED SEVENTY-ONE 31 41 1643 ONE THOUSAND SIX HUNDRED FORTY-THREE 31 53 1711 ONE THOUSAND SEVEN HUNDRED ELEVEN 29 59 2263 TWO THOUSAND TWO HUNDRED SIXTY-THREE 31 73 2449 TWO THOUSAND FOUR HUNDRED FORTY-NINE 31 79 4681 FOUR THOUSAND SIX HUNDRED EIGHTY-ONE 31 151 6119 SIX THOUSAND ONE HUNDRED NINETEEN 29 211 6641 SIX THOUSAND SIX HUNDRED FORTY-ONE 29 229 8711 EIGHT THOUSAND SEVEN HUNDRED ELEVEN 31 281 8903 EIGHT THOUSAND NINE HUNDRED THREE 29 307 So the answer sets are: 33, 253, 1007 and 33, 551, 1147 DECLARE FUNCTION verify! (s1\$, s2\$) DECLARE SUB ProcPiece (piece\$, MajorPower!) DATA one,two,three,four,five,six,seven,eight,nine DATA ten,eleven,twelve,thirteen,fourteen,fifteen,sixteen,seventeen DATA eighteen,nineteen DATA twenty,thirty,forty,fifty,sixty,seventy,eighty,ninety DATA thousand,million,billion,trillion,quadrillion,quintillion,sextillion DIM SHARED unit\$(19), ten\$(10), major\$(7) FOR i = 1 TO 19 READ unit\$(i) NEXT FOR i = 2 TO 9 READ ten\$(i) NEXT FOR i = 1 TO 7 READ major\$(i) NEXT DIM SHARED name\$, num\$, n CLS FOR n = 2 TO 9999 num\$ = LTRIM\$(RTRIM\$(STR\$(n))) IF num\$ = "0" THEN name\$ = "zero" ELSE name\$ = "" MajorPower = 0 DO l = LEN(num\$): IF l > 3 THEN l = 3 piece\$ = RIGHT\$(num\$, l) num\$ = LEFT\$(num\$, LEN(num\$) - l) CALL ProcPiece(piece\$, MajorPower) MajorPower = MajorPower + 1 LOOP WHILE LEN(num\$) > 0 END IF name1\$ = UCASE\$(name\$) name\$ = name1\$ DO i = verify(name\$, "ABCDEFGHIJKLMNOPQRSTUVWXYZ") IF i THEN name\$ = LEFT\$(name\$, i - 1) + MID\$(name\$, i + 1) LOOP UNTIL i = 0 l = LEN(name\$) IF n MOD l = 0 THEN pr = 1 FOR i = 2 TO SQR(l) IF l MOD i = 0 THEN pr = 0: EXIT FOR NEXT i IF pr THEN n2 = n \ l FOR i = 2 TO SQR(n2) IF n2 MOD i = 0 THEN pr = 0: EXIT FOR NEXT i IF pr THEN PRINT n; name1\$; l; n2 END IF END IF END IF NEXT SUB ProcPiece (piece\$, MajorPower) piece = VAL(piece\$) n\$ = "" IF piece > 99 THEN n\$ = unit\$(piece \ 100) + " hundred " piece = piece MOD 100 IF piece > 0 THEN n\$ = n\$ + "and " ' this to be commented out for part 2 ELSE IF MajorPower = 0 AND n > 999 THEN n\$ = n\$ + "and " ' likewise this END IF IF piece > 19 THEN n\$ = n\$ + ten\$(piece \ 10) piece = piece MOD 10 IF piece > 0 THEN n\$ = n\$ + "-": ELSE n\$ = n\$ + " " END IF IF piece > 0 THEN n\$ = n\$ + unit\$(piece) + " " IF n\$ > "" THEN name\$ = n\$ + major\$(MajorPower) + " " + name\$ END SUB FUNCTION verify (s1\$, s2\$) FOR i = 1 TO LEN(s1\$) IF INSTR(s2\$, MID\$(s1\$, i, 1)) = 0 THEN verify = i: EXIT FUNCTION NEXT verify = 0 END FUNCTION ``` Based upon Enigma No. 1614, "Letters & products", by Richard England, New Scientist, 25 September 2010. Subject Author Date solution Dej Mar 2010-12-07 06:30:47 1st couple -partial spoiler Ady TZIDON 2010-12-06 14:46:21 Please log in:

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