>>8730
>If you multiply c by small primes, the smoothness of BigN-n increase.
>Once the size of the product of small primes is larger than the root of c, when that product is multiplied by c, there is enough information to imply n.
>>8739
>which small primes are valid?
>>8744
>Avoid the use of two, use odd [alternating] primes.
Ok, think this is clear. Here is result for RSA2048:
1) take the first 233 primes (min number required while still providing enough 'information').
2) Remove alternating primes (so delete 3, 7, 13, 19, …). Result is this list of 116 primes:
BigInt[5, 11, 17, 23, 31, 41, 47, 59, 67, 73, 83, 97, 103, 109, 127, 137, 149, 157, 167, 179, 191, 197, 211, 227, 233, 241, 257, 269, 277, 283, 307, 313, 331, 347, 353, 367, 379, 389, 401, 419, 431, 439, 449, 461, 467, 487, 499, 509, 523, 547, 563, 571, 587, 599, 607, 617, 631, 643, 653, 661, 677, 691, 709, 727, 739, 751, 761, 773, 797, 811, 823, 829, 853, 859, 877, 883, 907, 919, 937, 947, 967, 977, 991, 1009, 1019, 1031, 1039, 1051, 1063, 1087, 1093, 1103, 1117, 1129, 1153, 1171, 1187, 1201, 1217, 1229, 1237, 1259, 1279, 1289, 1297, 1303, 1319, 1327, 1367, 1381, 1409, 1427, 1433, 1447, 1453, 1471]
3) Using BigInt/BigFloat, calculate product of these primes. Result is:
387690662375116154189306786300948040682152301112381332365947690358877016252291271579386805963882041509361136031463830160262212467528052601358967283927566989520797030933142943740776342583911079131737628443244072008838040734929847409534239275952452284284160980866268104515160752851645533924749226331947534836485
4) Test if product * sqrt_c c. If not, use more primes, if too large, trim list until min number of primes attained for list.
if sqrt_c < primeProd "OK, primeProd is larger than sqrt_c by", c - primeProd;
else "Add more primes, gap is", (c - primeProd);
end
Result for this list with RSA2048:
("OK, primeProd is larger than sqrt_c by", 25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987161491760058521104895835079161095536116271086072393115554792243877707807571989926584428204710928410151016170024737789515993921376615551232545447668706865200593860513521035480280148273931812271646970121373881700459124885651426525880377915555485715615600879464497755422866790625784918857287261170790874585883872)
>>8736
>Lets say you take the first fifteen primes and multiple c to make c'.
>You would focus on the column with e',d' and c'.
Did you mean multiply the primeProd result by sqrt_c here to get c'? Otherwise very large like the D value.