...  D.Pgms.maths.BigNum.RAMCABI


 YES.Tue,06 Jan 2004.00:39:42
BBC Basic V Progm  $..calc.factors.lgefactor.PrimeCabi, /6/94, /3/95 3.05.98
31.8.02, 5.01.04
 by Donald S  McDonald, 63/3 Hutchison Rd, NEWTOWN, Wellington 2
 New Zealand.   Phone 64(NZ) +4(WN-) + 389-6820.


Solve for (odd) factors, p <= 2^16.5 = 92,681.
 of Large Numbers > 2E9 of special type ..

         ABS(    C * a^b -i  )   <=   n  MOD p,     Progm "PrimeCabi"
   multiplier * (base ^ index) + offset  <=  neighbourhood.

Would you like to see some samples, examples?  Yy ( N) ? 

PROC input.

enter text, formula.  Analysis of c, a, b, i, n  later : ?bb
      multiplier * (base ^ index) + offset  <=  neighbourhood.
        2E9          2E9    2E9      2E9           2^5.  

enter base ( expression a$ , max= 2E9, often 2 default, 10, 2^10, 1E3. ) ?1E9
a$ = 1E9 = 1000000000

enter index (power b%, [default 1]) ?1E9
enter multiplier, c% (default = 1) ?
1.000000000
enter offset, +/- i% = EVAL i$ (default  0) ?
 = 0.000000000
enter neighbourhood (sm. latitude) <= n%,  (default = 0 ) ?200


find (first)factors p, satisfying ,  S% =  bb
 ABS( 1.000000000 * 1000000000 ^ 1000000000 + 0.000000000 )  <= 200  MOD p.

PROC binary ( 1E9
500000000 ,  0
250000000 ,  0
125000000 ,  0
62500000 ,  0
31250000 ,  0
15625000 ,  0
7812500 ,  0
3906250 ,  0
1953125 ,  0
976562 ,  1
488281 ,  0
244140 ,  1
122070 ,  0
61035 ,  0
30517 ,  1
15258 ,  1
7629 ,  0
3814 ,  1
1907 ,  0
953 ,  1
476 ,  1
238 ,  0
119 ,  0
59 ,  1
29 ,  1
14 ,  1
7 ,  0
3 ,  1
1 ,  1
0 ,  1

PROC mult.
TEST FACTORS.

S% = 0  factor = 2  FIRST  = 2 * 1PRIME. (test dup. factors).  
S% = 0  factor = 4   = 2 * 2  contin cs.= 7    

S% = 0  factor = 8   = 2 * 4  contin cs.= 209    

S% = 0  factor = 16   = 2 * 8 = 4 * 4  contin cs.= 241    

S% = 0  factor = 32   = 2 * 16 = 4 * 8  contin cs.= 249    

S% = 0  factor = 64   = 2 * 32 = 4 * 16 = 8 * 8  contin cs.= 257    

S% = 0  factor = 128   = 2 * 64 = 4 * 32 = 8 * 16  contin cs.= 265    

S% = 0  factor = 256   = 2 * 128 = 4 * 64 = 8 * 32 = 16 * 16  contin cs.= 273    

S% = 0  factor = 512   = 2 * 256 = 4 * 128 = 8 * 64 = 16 * 32  contin cs.= 281    

S% = 0  factor = 1024   = 2 * 512 = 4 * 256 = 8 * 128 = 16 * 64 = 32 * 32  contin cs.= 289    

S% = 0  factor = 2048   = 2 * 1024 = 4 * 512 = 8 * 256 = 16 * 128 = 32 * 64  contin cs.= 297    

S% = 0  factor = 4096   = 2 * 2048 = 4 * 1024 = 8 * 512 = 16 * 256 = 32 * 128 = 64 * 64  contin cs.= 305    

S% = 0  factor = 8192   = 2 * 4096 = 4 * 2048 = 8 * 1024 = 16 * 512 = 32 * 256 = 64 * 128  contin cs.= 314    

S% = 0  factor = 16384   = 2 * 8192 = 4 * 4096 = 8 * 2048 = 16 * 1024 = 32 * 512 = 64 * 256 = 128 * 128  contin cs.= 322    

S% = 0  factor = 32768   = 2 * 16384 = 4 * 8192 = 8 * 4096 = 16 * 2048 = 32 * 1024 = 64 * 512 = 128 * 256  contin cs.= 330    
  contin cs.= 336    

S% = 1  factor = 3  FIRST  = 3 * 1PRIME. (test dup. factors).  
S% = 1  factor = 9   = 3 * 3  contin cs.= 346    

S% = 1  factor = 27   = 3 * 9  contin cs.= 353    

S% = 1  factor = 81   = 3 * 27 = 9 * 9  contin cs.= 361    

S% = 82  factor = 243  FIRST  = 3 * 81 = 9 * 27  contin cs.= 369    

S% = 82  factor = 729   = 3 * 243 = 9 * 81 = 27 * 27  contin cs.= 377    
  contin cs.= 385    

S% = 0  factor = 5  PRIME. (test dup. factors).  
S% = 0  factor = 25   = 5 * 5  contin cs.= 394    

S% = 0  factor = 125   = 5 * 25  contin cs.= 401    

S% = 0  factor = 625   = 5 * 125 = 25 * 25  contin cs.= 409    

S% = 0  factor = 3125   = 5 * 625 = 25 * 125  contin cs.= 417    

S% = 0  factor = 15625   = 5 * 3125 = 25 * 625 = 125 * 125  contin cs.= 425    
  contin cs.= 432    

S% = 1  factor = 7  PRIME. (test dup. factors).  
S% = 15  factor = 49  FIRST  = 7 * 7  contin cs.= 442    

S% = -34  factor = 343  FIRST  = 7 * 49  contin cs.= 449    
  contin cs.= 457    

S% = 1  factor = 9   = 3 * 3  contin cs.= 465    

S% = 1  factor = 11  PRIME. (test dup. factors).  
S% = -21  factor = 121  FIRST  = 11 * 11  contin cs.= 474    
  contin cs.= 481    

S% = 1  factor = 13  PRIME. (test dup. factors).  
S% = -38  factor = 169  FIRST  = 13 * 13  contin cs.= 490    
  contin cs.= 497    

S% = -5  factor = 15  FIRST  = 3 * 5  contin cs.= 505    

S% = 1  factor = 17  PRIME. (test dup. factors).  
S% = 103  factor = 289  FIRST  = 17 * 17  contin cs.= 514    
  contin cs.= 521    

S% = 1  factor = 19  PRIME. (test dup. factors).  
S% = 39  factor = 361  FIRST  = 19 * 19  contin cs.= 530    
  contin cs.= 537    

S% = 1  factor = 21   = 3 * 7  contin cs.= 545    

S% = 8  factor = 23  FIRST PRIME. (test dup. factors).  
S% = -61  factor = 529  FIRST  = 23 * 23  contin cs.= 554    
  contin cs.= 608    

S% = 0  factor = 25   = 5 * 5  contin cs.= 640    

S% = 1  factor = 27   = 3 * 9  contin cs.= 648    

S% = -9  factor = 29  FIRST PRIME. (test dup. factors).    contin cs.= 657    

S% = 1  factor = 31  PRIME. (test dup. factors).    contin cs.= 665    

S% = 1  factor = 33   = 3 * 11  contin cs.= 672    

S% = 15  factor = 35   = 5 * 7  contin cs.= 680    

S% = 1  factor = 37  PRIME. (test dup. factors).    contin cs.= 689    

S% = 1  factor = 39   = 3 * 13  contin cs.= 696    

S% = 1  factor = 41  PRIME. (test dup. factors).    contin cs.= 705    
.........



S% = 135  factor = 38809   = 197 * 197  contin cs.= 10922    

S% = 1  factor = 38897   = 97 * 401  contin cs.= 10941    

S% = 1  factor = 39101   = 61 * 641  contin cs.= 10979    

S% = -1  factor = 39937  FIRST PRIME. (test dup. factors).    contin cs.= 11137    

S% = 34  factor = 40153  PRIME. (test dup. factors).    contin cs.= 11180    

S% = -30  factor = 40279   = 47 * 857  contin cs.= 11205    
40375, 
S% = 1  factor = 40501   = 101 * 401  contin cs.= 11249    

S% = 177  factor = 40577  PRIME. (test dup. factors).    contin cs.= 11265    

S% = 1  factor = 40723   = 193 * 211  contin cs.= 11294    

S% = 1  factor = 40921   = 151 * 271  contin cs.= 11333    

S% = 1  factor = 40961  PRIME. (test dup. factors).    contin cs.= 11341    

S% = 112  factor = 40993  PRIME. (test dup. factors).    contin cs.= 11350    

S% = 1  factor = 41059   = 19 * 2161  contin cs.= 11365    

S% = 1  factor = 42121   = 73 * 577  contin cs.= 11560    

S% = -46  factor = 42401   = 109 * 389  contin cs.= 11614    

S% = 1  factor = 42517   = 17 * 2501 = 41 * 1037 = 61 * 697  contin cs.= 11639    

S% = 1  factor = 42661   = 37 * 1153  contin cs.= 11669    

S% = 1  factor = 42769   = 19 * 2251  contin cs.= 11690    

S% = 1  factor = 42883   = 19 * 2257 = 37 * 1159 = 61 * 703  contin cs.= 11716    

S% = 1  factor = 42997   = 19 * 2263 = 31 * 1387 = 73 * 589  contin cs.= 11737    

S% = 1  factor = 43201  PRIME. (test dup. factors).    contin cs.= 11777    

S% = 1  factor = 43553   = 97 * 449  contin cs.= 11843    

S% = 1  factor = 43621   = 181 * 241  contin cs.= 11859    

S% = 1  factor = 43679   = 31 * 1409  contin cs.= 11871   

Escape     find factors p, satisfying
 ABS( 1.000000000 * 1000000000 ^ 1000000000 + 0.000000000 )  <= 200  MOD p.
highest factor tested,  P% = 43679    cs. = 12260   at ERL.  =  1430

summary factors, enter cont.?

sumry factors,  S% = 0       2   cont.   
sumry factors,  S% = -1      39937      S% = +1   3   cont.   
sumry factors,  S% = -2      1753       S% = +2   34807   cont.   
sumry factors,  S% = -3      0          S% = +3   29147   cont.   
sumry factors,  S% = -4      157        S% = +4   127   cont.   
sumry factors,  S% = -5      15         S% = +5   379   cont.   
sumry factors,  S% = -6      0          S% = +6   1483   cont.   ,
sumry factors,  S% = -8      59         S% = +8   23   cont.   
sumry factors,  S% = -9      29   cont.   
sumry factors,  S% = -10     0          S% = +10  45   cont.   
sumry factors,  S% = -11     89         S% = +11  523   cont.   
sumry factors,  S% = -12     1093       S% = +12  431   cont.   
sumry factors,  S% = -13     0          S% = +13  179   cont.   
sumry factors,  S% = -14     619   cont.   
sumry factors,  S% = -15     83         S% = +15  49   cont.   
sumry factors,  S% = -16     17681      S% = +16  113   cont.   
sumry factors,  S% = -17     53         S% = +17  47   cont.   
sumry factors,  S% = -18     6971   cont.   
sumry factors,  S% = -19     313   cont.   
sumry factors,  S% = -20     0          S% = +20  551   cont.   
sumry factors,  S% = -21     121        S% = +21  43   cont.   
sumry factors,  S% = -22     20107   cont.   
sumry factors,  S% = -23     3527       S% = +23  317   cont.   
sumry factors,  S% = -24     0          S% = +24  269   cont.   
sumry factors,  S% = -25     0          S% = +25  409   cont.   
sumry factors,  S% = -26     10181   cont.   
sumry factors,  S% = -27     1069       S% = +27  3697   cont.   
sumry factors,  S% = -28     757   cont.   ,
sumry factors,  S% = -30     631        S% = +30  107   cont.   ,
sumry factors,  S% = -32     0          S% = +32  71   cont.   
sumry factors,  S% = -33     79   cont.   
sumry factors,  S% = -34     343        S% = +34  12829   cont.   ,
sumry factors,  S% = -36     0          S% = +36  937   cont.   ,
sumry factors,  S% = -38     169        S% = +38  31321   cont.   
sumry factors,  S% = -39     0          S% = +39  361   cont.   
sumry factors,  S% = -40     733        S% = +40  8563   cont.   
sumry factors,  S% = -41     15277   cont.   
sumry factors,  S% = -42     337        S% = +42  593   cont.   ,
sumry factors,  S% = -44     487        S% = +44  26717   cont.   
sumry factors,  S% = -45     0          S% = +45  1091   cont.   
sumry factors,  S% = -46     109        S% = +46  7937   cont.   ,,
sumry factors,  S% = -49     0          S% = +49  557   cont.   
sumry factors,  S% = -50     457   cont.   ,
sumry factors,  S% = -52     1433       S% = +52  139   cont.   
sumry factors,  S% = -53     479        S% = +53  163   cont.   
sumry factors,  S% = -54     5953   cont.   ,
sumry factors,  S% = -56     227   cont.   
sumry factors,  S% = -57     5851       S% = +57  739   cont.   
sumry factors,  S% = -58     419   cont.   
sumry factors,  S% = -59     2729       S% = +59  281   cont.   ,
sumry factors,  S% = -61     529   cont.   
sumry factors,  S% = -62     197   cont.   
sumry factors,  S% = -63     0          S% = +63  131   cont.   
sumry factors,  S% = -64     229        S% = +64  823   cont.   
sumry factors,  S% = -65     0          S% = +65  853   cont.   
sumry factors,  S% = -66     0          S% = +66  349   cont.   
sumry factors,  S% = -67     493   cont.   
sumry factors,  S% = -68     0          S% = +68  1109   cont.   ,
sumry factors,  S% = -70     503   cont.   
sumry factors,  S% = -71     22039      S% = +71  283   cont.   
sumry factors,  S% = -72     13187      S% = +72  3041   cont.   
sumry factors,  S% = -73     10979   cont.   
sumry factors,  S% = -74     1009   cont.   ,
sumry factors,  S% = -76     0          S% = +76  17327   cont.   
sumry factors,  S% = -77     5029       S% = +77  437   cont.   
sumry factors,  S% = -78     199        S% = +78  2581   cont.   
sumry factors,  S% = -79     4861   cont.   ,
sumry factors,  S% = -81     6481       S% = +81  167   cont.   
sumry factors,  S% = -82     263        S% = +82  243   cont.   
sumry factors,  S% = -83     383   cont.   
sumry factors,  S% = -84     391   cont.   ,
sumry factors,  S% = -86     809   cont.   
sumry factors,  S% = -87     1013   cont.   
sumry factors,  S% = -88     983   cont.   
sumry factors,  S% = -89     0          S% = +89  2293   cont.   ,,
sumry factors,  S% = -92     0          S% = +92  7351   cont.   
sumry factors,  S% = -93     36653      S% = +93  3251   cont.   
sumry factors,  S% = -94     16067   cont.   
sumry factors,  S% = -95     2833   cont.   
sumry factors,  S% = -96     683        S% = +96  883   cont.   
sumry factors,  S% = -97     3413   cont.   
sumry factors,  S% = -98     1811       S% = +98  239   cont.   ,
sumry factors,  S% = -100    8989       S% = +100 4093   cont.   
sumry factors,  S% = -101    0          S% = +101 521   cont.   
sumry factors,  S% = -102    0          S% = +102 4003   cont.   
sumry factors,  S% = -103    0          S% = +103 289   cont.   
sumry factors,  S% = -104    839   cont.   ,
sumry factors,  S% = -106    0          S% = +106 2917   cont.   
sumry factors,  S% = -107    3547       S% = +107 1247   cont.   ,
sumry factors,  S% = -109    0          S% = +109 373   cont.   
sumry factors,  S% = -110    26569   cont.   
sumry factors,  S% = -111    0          S% = +111 331   cont.   
sumry factors,  S% = -112    9661       S% = +112 587   cont.   
sumry factors,  S% = -113    277        S% = +113 311   cont.   
sumry factors,  S% = -114    5297   cont.   
sumry factors,  S% = -115    0          S% = +115 919   cont.   ,
sumry factors,  S% = -117    3301   cont.   ,
sumry factors,  S% = -119    3719       S% = +119 941   cont.   ,
sumry factors,  S% = -121    0          S% = +121 1193   cont.   
sumry factors,  S% = -122    0          S% = +122 7253   cont.   
sumry factors,  S% = -123    1643       S% = +123 1403   cont.   ,
sumry factors,  S% = -125    1129       S% = +125 569   cont.   ,
sumry factors,  S% = -127    0          S% = +127 3389   cont.   
sumry factors,  S% = -128    0          S% = +128 3391   cont.   
sumry factors,  S% = -129    0          S% = +129 541   cont.   ,
sumry factors,  S% = -131    3671       S% = +131 547   cont.   
sumry factors,  S% = -132    0          S% = +132 8677   cont.   ,,
sumry factors,  S% = -135    0          S% = +135 38809   cont.   ,
sumry factors,  S% = -137    0          S% = +137 439   cont.   
sumry factors,  S% = -138    2017       S% = +138 1327   cont.   ,,
sumry factors,  S% = -141    31253   cont.   
sumry factors,  S% = -142    3931   cont.   ,
sumry factors,  S% = -144    15461      S% = +144 1597   cont.   
sumry factors,  S% = -145    14389   cont.   ,
sumry factors,  S% = -147    0          S% = +147 709   cont.   
sumry factors,  S% = -148    0          S% = +148 1373   cont.   
sumry factors,  S% = -149    499        S% = +149 2053   cont.   ,
sumry factors,  S% = -151    817   cont.   
sumry factors,  S% = -152    0          S% = +152 421   cont.   
sumry factors,  S% = -153    4447       S% = +153 2983   cont.   
sumry factors,  S% = -154    899   cont.   
sumry factors,  S% = -155    10589   cont.   ,
sumry factors,  S% = -157    0          S% = +157 829   cont.   
sumry factors,  S% = -158    719        S% = +158 2753   cont.   
sumry factors,  S% = -159    827        S% = +159 463   cont.   
sumry factors,  S% = -160    1663       S% = +160 1889   cont.   
sumry factors,  S% = -161    0          S% = +161 1993   cont.   ,
sumry factors,  S% = -163    2969       S% = +163 6983   cont.   ,
sumry factors,  S% = -165    0          S% = +165 1189   cont.   ,
sumry factors,  S% = -167    0          S% = +167 701   cont.   
sumry factors,  S% = -168    6379       S% = +168 20549   cont.   
sumry factors,  S% = -169    1061       S% = +169 647   cont.   
sumry factors,  S% = -170    347   cont.   
sumry factors,  S% = -171    0          S% = +171 2803   cont.   
sumry factors,  S% = -172    821        S% = +172 2071   cont.   ,
sumry factors,  S% = -174    0          S% = +174 33377   cont.   ,
sumry factors,  S% = -176    1219   cont.   
sumry factors,  S% = -177    509        S% = +177 443   cont.   ,
sumry factors,  S% = -179    1451       S% = +179 5179   cont.   
sumry factors,  S% = -180    5827   cont.   
sumry factors,  S% = -181    5893       S% = +181 461   cont.   
sumry factors,  S% = -182    10553   cont.   ,
sumry factors,  S% = -184    3959       S% = +184 20731   cont.   
sumry factors,  S% = -185    1829       S% = +185 1087   cont.   
sumry factors,  S% = -186    1139       S% = +186 1229   cont.   ,
sumry factors,  S% = -188    1319   cont.   
sumry factors,  S% = -189    1691   cont.   
sumry factors,  S% = -190    3167       S% = +190 613   cont.   
sumry factors,  S% = -191    0          S% = +191 2641   cont.   
sumry factors,  S% = -192    0          S% = +192 4117   cont.   
sumry factors,  S% = -193    5209   cont.   
sumry factors,  S% = -194    0          S% = +194 3799   cont.   
sumry factors,  S% = -195    0          S% = +195 5141   cont.   
sumry factors,  S% = -196    3361       S% = +196 5347   cont.   
sumry factors,  S% = -197    7457       S% = +197 6761   cont.   
sumry factors,  S% = -198    3881       S% = +198 433   cont.   
sumry factors,  S% = -199    3013   cont.   ,

BBC Basic V Program  $.donmcd.calc.normal.PrimeCabi,  e n d .  17/6/94,  5.01.04.
RUN AGAIN, Enter G/go, else <RETurn> end.?
