>>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.

Using this method >>8755

for RSA100:

c = 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139

Provides list of 26 primes:

[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]

These are our "Helper" primes, our friends on the Grid.

Product of the Helpers:

primeProd = 41257856375896281668876416228583805794533827727585

Now, for the Helper c (c') we will call cQ = primeProd * c

cQ = 62819419559245428990590666648167912190753692290005426173804705886475986730546752279947003199446823008746292532203222745368434870226476085407239644315

Then, running this cQ through the Test program provided provides:

c = 62819419559245428990590666648167912190753692290005426173804705886475986730546752279947003199446823008746292532203222745368434870226476085407239644315

d_raw = 250638024966774403025013316223313816646669634534476971992571474945100141137.8477

d = 250638024966774403025013316223313816646669634534476971992571474945100141137

d^2 = 62819419559245428990590666648167912190753692290005426173804705886475986730122196691381219796056678466160777063949696723671284885418579019077953519616.0000

(d+1)^2 = 62819419559245428990590666648167912190753692290005426173804705886475986730623097834245891753493543307621394463186788408435522860046054377144411226112.0000

e = 424555588565783403390144542585515468253526021697149984807897066329286124699

a = 1

b = 62819419559245428990590666648167912190753692290005426173804705886475986730547123410460421227321461515089448967006206600869871244846825310488828575744

f = -76345554298888554046720298875101930983565663067087989819578291737171581797

x = 250638024966774403025013316223313816646669634534476971992571474945100141136

X = 62819419559245428990590666648167912190753692290005426173804705886475986729620412124984158646455021975949788205454691296958609101312042857910849503232.0000

Xpe = 62819419559245428990590666648167912190753692290005426173804705886475986730045338844063360077719805024878460108511201174157195460740289149321724559360.0000

Half_Xpe = 31409709779622714495295333324083956095376846145002713086902352943237993365022669422031680038859902512439230054255600587078597730370144574660862279680.0000

n = 31409709779622714495295333324083956095376846145002713086902352943237993365022669422031680038859902512439230054255600587078597730370144574660862279680

dpn = 31409709779622714495295333324083956095376846145002713086902352943237993365273119993464016017578334933169538753874146429460716717683882253694091132928

DPN = 986569868440126791986193534547739745680544007989124346659614805260975644490424274974780234053208940545490504751842760925502448328942543703363993300433751046989999127500313979973409365100438103716848552572009664106794849873336995774593749279083475218738252059496372285076090360868430678887772454912.0000

DPNmc = 986569868440126791986193534547739745680544007989124346659614805260975644490424274974780234053208940545490504751842760925502448328942543703363993300433751046989999127500313979973409365100438103716848552572009664106794849873336995774593749279083475218738252059496372285076090360868430678887772454912.0000

rtDPNmc = 31409709779622714495295333324083956095376846145002713086902352943237993365273119993464016017578334933169538753874146429460716717683882253694091132928.000000000

rtDPNmc_minusx = 31409709779622714495295333324083956095376846145002713086902352943237993365022669422031680038859902512439230054255600587078597730370144574660862279680.000000000

mid_a_b_gap = -441711766194596082395824375185729628956870974218904739530401550323154944.00

Your rtDPNmc_minusx - n = ZERO! Yes, 0.0

You passed the Test, you may enter the GRID!

>>8771

Also, can see why we need larger numbers.

For our friend 6107, only need first 3 primes in the series:

[5, 11, 17]

primeProduct = 935

cQ = 5710045 (for c=6107)

c = 5710045

d_raw = 2389.5700

d = 2389

d^2 = 5707321.0000

(d+1)^2 = 5712100.0000

e = 2724

a = 1

b = 5710045

f = -2055

x = 2388

X = 5702544.0000

Xpe = 5705268.0000

Half_Xpe = 2852634.0000

n = 2852634

dpn = 2855023

DPN = 8151156330529.0000

DPNmc = 8151150620484.0000

rtDPNmc = 2855022.000000000

rtDPNmc_minusx = 2852634.000000000

mid_a_b_gap = 1.00

Your rtDPNmc_minusx - n = ZERO! Yes, 0.0

You passed the Test, you may enter the GRID!

For our friend 145, only need first 2 primes in the series:

[5, 11]

primeProduct = 55

cQ = 7975 (for c=145)

c = 7975

d_raw = 89.3029

d = 89

d^2 = 7921.0000

(d+1)^2 = 8100.0000

e = 54

a = 1

b = 7975

f = -125

x = 88

X = 7744.0000

Xpe = 7798.0000

Half_Xpe = 3899.0000

n = 3899

dpn = 3988

DPN = 15904144.0000

DPNmc = 15896169.0000

rtDPNmc = 3987.000000000

rtDPNmc_minusx = 3899.000000000

mid_a_b_gap = 1.00

Your rtDPNmc_minusx - n = ZERO! Yes, 0.0

You passed the Test, you may enter the GRID!

>>8733 hope this is starting to click for you MA. And, it's Fryday!

>>8721

>So, what I'll add tonight, as well as answering questions between now and Sunday, is the code to calculate (For any size) the difference between BigN and n for known RSA numbers. At that scale, you will see a Revelation.

Would be good if you could stop in this eve, time is limited this week. ty.

>>8773

Frankly, don't think it matters overall.

Perhaps for the 6107 case, if instead of:

primeProd1 = [5 * 11 * 17] = 935, we used

primeProd2 = [13 * 17 * 17] = 3757?

Would there still be enough information with the repeated factor (17) to collapse the grid, where n falls out? Would larger factors be useful here?

Future proves past on these questions perhaps.

>>8772

If anyone would like some 6107 coupled with 3757 helper group, generated a few. (pic example). Rather than clutter thread, here's a pastebin to "c6107cQ3757_factorization":

https://pastebin.com/gTrvQk7N

>>8775

Care to expound?