**** Prime Order *** y^2 = x^3 + 172358387239013*x + 200408220530617 (mod 281474976710677) y = 39907781747663 Order = 281474976719383 /* var modulus = 281474976710677; var len = 114; var min = Math.ceil( ( modulus + 1 ) - 1.4 * Math.sqrt( modulus ) ); var max = Math.floor( ( modulus + 1 ) + 1.4 * Math.sqrt( modulus ) ); var p0 = min / Math.log( min ); var p1 = max / Math.log( max ); _debug(Math.log( modulus ) * 7 * ( ( p1 - p0 ) / len )); var modulus = 281474976710677; var a = 172358387239013; var b0 = 200408220530617; 5.0238168883390040210330961954841 @ Prime DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220001100 DEBUG: range : 8900 DEBUG: --- DEBUG: minBinString : 1000000000000000000000000000000000000000000010101 DEBUG: maxBinString : 1000000000000000000000000000000000010011010001001 DEBUG: comBinString : 1000000000000000000000000000000000000000000000000 DEBUG: 14 : 49 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 15 ms DEBUG: *Cost ( 4485 / 8900 b's tested ): 6264134 ms DEBUG: --- DEBUG: End b : 200408220009999 DEBUG: ** Total Cost: 6264.149 seconds DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220010000 DEBUG: range : 10000 DEBUG: --- DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 16 ms DEBUG: *Cost ( 4848 / 10000 b's tested ): 7007877 ms DEBUG: --- DEBUG: End b : 200408220019999 DEBUG: ** Total Cost: 7007.893 seconds DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220020000 DEBUG: range : 100 DEBUG: --- DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 0 ms DEBUG: *Cost ( 45 / 100 b's tested ): 43625 ms DEBUG: --- DEBUG: End b : 200408220020099 DEBUG: ** Total Cost: 43.625 seconds 1.3H/10000 DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220020000 DEBUG: range : 100 DEBUG: --- DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 15 ms DEBUG: *Cost ( 45 / 100 b's tested ): 70866 ms DEBUG: --- DEBUG: End b : 200408220020099 DEBUG: ** Total Cost: 70.881 seconds 2.2H/10000 DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220020000 DEBUG: range : 100 DEBUG: --- DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 16 ms DEBUG: *Cost ( 45 / 100 b's tested ): 41000 ms DEBUG: --- DEBUG: End b : 200408220020099 DEBUG: ** Total Cost: 41.016 seconds DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220020100 DEBUG: range : 9900 DEBUG: --- DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 16 ms DEBUG: *Cost ( 5001 / 9900 b's tested ): 4705050 ms DEBUG: --- DEBUG: End b : 200408220029999 DEBUG: ** Total Cost: 4705.066 seconds 1.3H/10000 DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220030000 DEBUG: range : 10000 DEBUG: --- DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 0 ms DEBUG: *Cost ( 4988 / 10000 b's tested ): 4679556 ms DEBUG: --- DEBUG: End b : 200408220039999 DEBUG: ** Total Cost: 4679.556 seconds DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220040000 DEBUG: range : 5000 DEBUG: --- DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 16 ms DEBUG: *Cost ( 2520 / 5000 b's tested ): 2294439 ms DEBUG: --- DEBUG: End b : 200408220044999 DEBUG: ** Total Cost: 2294.455 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220045000 DEBUG: range : 5000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 15 ms DEBUG: *Cost ( 2484 / 5000 b's tested ): 2287638 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220049999 DEBUG: ** Total Cost: 2287.653 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220050000 DEBUG: range : 65000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 16 ms DEBUG: *Cost ( 32445 / 65000 b's tested ): 32709947 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220114999 DEBUG: ** Total Cost: 32709.963 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220115000 DEBUG: range : 5000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 0 ms DEBUG: *Cost ( 2449 / 5000 b's tested ): 2533280 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220119999 DEBUG: ** Total Cost: 2533.28 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220120000 DEBUG: range : 10000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 16 ms DEBUG: *Cost ( 5096 / 10000 b's tested ): 6299552 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220129999 DEBUG: ** Total Cost: 6299.568 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220130000 DEBUG: range : 10000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 16 ms DEBUG: *Cost ( 5058 / 10000 b's tested ): 6262650 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220139999 DEBUG: ** Total Cost: 6262.666 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220140000 DEBUG: range : 10000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 31 ms DEBUG: *Cost ( 4857 / 10000 b's tested ): 5966307 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220149999 DEBUG: ** Total Cost: 5966.338 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220150000 DEBUG: range : 10000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 16 ms DEBUG: *Cost ( 4961 / 10000 b's tested ): 4526449 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220159999 DEBUG: ** Total Cost: 4526.465 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220160000 DEBUG: range : 10000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 16 ms DEBUG: *Cost ( 5055 / 10000 b's tested ): 4658882 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220169999 DEBUG: ** Total Cost: 4658.898 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220170000 DEBUG: range : 10000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 16 ms DEBUG: *Cost ( 5045 / 10000 b's tested ): 4629738 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220179999 DEBUG: ** Total Cost: 4629.754 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220180000 DEBUG: range : 60000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 0 ms DEBUG: *Cost ( 29746 / 60000 b's tested ): 27071266 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220239999 DEBUG: ** Total Cost: 27071.266 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220240000 DEBUG: range : 10000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 16 ms DEBUG: *Cost ( 4937 / 10000 b's tested ): 4542307 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220249999 DEBUG: ** Total Cost: 4542.323 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220250000 DEBUG: range : 60000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 0 ms DEBUG: *Cost ( 30180 / 60000 b's tested ): 27635582 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220309999 DEBUG: ** Total Cost: 27635.582 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220310000 DEBUG: range : 60000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 0 ms DEBUG: *Cost ( 30132 / 60000 b's tested ): 27410039 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220369999 DEBUG: ** Total Cost: 27410.039 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220370000 DEBUG: range : 10000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 0 ms DEBUG: *Cost ( 4909 / 10000 b's tested ): 4915384 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220379999 DEBUG: ** Total Cost: 4915.384 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220380000 DEBUG: range : 10000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 0 ms DEBUG: *Cost ( 4941 / 10000 b's tested ): 4548527 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220389999 DEBUG: ** Total Cost: 4548.527 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220390000 DEBUG: range : 10000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 15 ms DEBUG: *Cost ( 5070 / 10000 b's tested ): 4719886 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220399999 DEBUG: ** Total Cost: 4719.901 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220400000 DEBUG: range : 60000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 16 ms DEBUG: *Cost ( 29975 / 60000 b's tested ): 27347620 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220459999 DEBUG: ** Total Cost: 27347.652 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220460000 DEBUG: range : 30000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 15 ms DEBUG: *Cost ( 15010 / 30000 b's tested ): 13974177 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220489999 DEBUG: ** Total Cost: 13974.192 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220490000 DEBUG: range : 10000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 0 ms DEBUG: *Cost ( 5010 / 10000 b's tested ): 4637606 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220499999 DEBUG: ** Total Cost: 4637.606 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220500000 DEBUG: range : 10000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 15 ms DEBUG: *Cost ( 5010 / 10000 b's tested ): 4576206 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220509999 DEBUG: ** Total Cost: 4576.221 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220510000 DEBUG: range : 10000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 0 ms DEBUG: *Cost ( 5037 / 10000 b's tested ): 5181918 ms DEBUG: --- FAILED --- DEBUG: End b : 200408220519999 DEBUG: ** Total Cost: 5181.918 seconds DEBUG: --- BEGIN --- DEBUG: modulus = 281474976710677 : 48-bit DEBUG: Initial b : 200408220520000 DEBUG: range : 60000 DEBUG: zero_bias : 7 / 14 DEBUG: Num of primes used : 114 / 114 DEBUG: *Cost ( pre-processing ): 15 ms DEBUG: *Cost ( 5278 / 10618 b's tested ): 4822668 ms DEBUG: --- SUCCESS! --- DEBUG: End b : 200408220530617 DEBUG: ** Total Cost: 4822.683 seconds **** Prime Order *** y^2 = x^3 + 172358387239013*x + 200408220530617 (mod 281474976710677) y = 39907781747663 Order = 281474976719383