5.998490465869538X10^615 =

1.816968190853090X10^205. * 3.3013734065719492767310020297X10^410

May not be exact to digit but magnitude is there.

]]>3333333333333333333333333333333333333333333333333333333333333333333333\

3333333333333333333333333333333333333333333333333333333333333333333

256 < 2048 by quite a bit • September 23, 2019 6:24 AM

Two 128 bit primes multiplied looks like:

69,420,827,571,959,709,546,340,695,189,354,893,943,777,501,940,316,291,649,816,713,221,998,382,139,059

Two 1024 bit primes multiplied looks like:

19,343,667,891,781,738,797,370,449,870,396,728,863,202,179,703,682,342,733,967,278,822,480,775,276,979,813,504,845,595,034,120,393,370,152,899,748,537,330,898,548,017,116,175,240,963,843,867,106,157,651,562,938,898,587,956,984,439,585,038,390,081,531,059,793,636,342,757,112,708,239,493,995,608,005,284,452,393,526,826,826,070,437,900,649,990,778,255,928,880,967,794,060,642,207,210,135,237,248,313,591,984,445,102,205,903,536,129,280,729,693,873,645,010,158,968,436,202,325,737,975,359,495,133,351,478,385,069,986,802,247,946,708,263,098,835,744,821,961,101,805,321,686,249,554,702,982,917,404,602,650,552,634,211,721,543,194,027,909,462,103,211,831,759,214,437,760,483,022,798,117,868,041,446,071,398,803,987,275,533,080,729,349,251,435,281,331,126,580,312,335,348,000,444,123,257,382,275,855,627,368,919,052,416,438,211

Just a tad harder.

Keep making fun of these fraudsters: Clown Turdling

I’m getting close and I’m only using Mathematica and guessing.

In[118]:= PNP = \

1934366789178173879737044987039672886320217970368234273396727882248077\

5276979813504845595034120393370152899748537330898548017116175240963843\

8671061576515629388985879569844395850383900815310597936363427571127082\

3949399560800528445239352682682607043790064999077825592888096779406064\

2207210135237248313591984445102205903536129280729693873645010158968436\

2023257379753594951333514783850699868022479467082630988357448219611018\

0532168624955470298291740460265055263421172154319402790946210321183175\

9214437760483022798117868041446071398803987275533080729349251435281331\

126580312335348000444123257382275855627368919052416438211

x = PNP * (1/

833333333333333333333333333333333333333333333333333333333333333333\

3333333333333333333333333333333333333333333333333333333333333333333333\

3333333333333333333333333333333333333333333333333333333333333333333333\

3)

Sqrt[((((x^2 * PNP^4 + 2* PNP^2 * x^5) + x^8) /

PNP^4) * ((PNP^2/ x^2)))]

Out[118]= \

1934366789178173879737044987039672886320217970368234273396727882248077\

5276979813504845595034120393370152899748537330898548017116175240963843\

8671061576515629388985879569844395850383900815310597936363427571127082\

3949399560800528445239352682682607043790064999077825592888096779406064\

2207210135237248313591984445102205903536129280729693873645010158968436\

2023257379753594951333514783850699868022479467082630988357448219611018\

0532168624955470298291740460265055263421172154319402790946210321183175\

9214437760483022798117868041446071398803987275533080729349251435281331\

126580312335348000444123257382275855627368919052416438211

Out[119]= \

1934366789178173879737044987039672886320217970368234273396727882248077\

5276979813504845595034120393370152899748537330898548017116175240963843\

8671061576515629388985879569844395850383900815310597936363427571127082\

3949399560800528445239352682682607043790064999077825592888096779406064\

2207210135237248313591984445102205903536129280729693873645010158968436\

2023257379753594951333514783850699868022479467082630988357448219611018\

0532168624955470298291740460265055263421172154319402790946210321183175\

9214437760483022798117868041446071398803987275533080729349251435281331\

126580312335348000444123257382275855627368919052416438211/\

8333333333333333333333333333333333333333333333333333333333333333333333\

3333333333333333333333333333333333333333333333333333333333333333333333\

3333333333333333333333333333333333333333333333333333333333333333333

Out[120]= \

1119462642967601379625749889949236065777407216363091843656817758630897\

2822004013012808616251428523303469194983368339224288931527755260370593\

4564726982165021366914927214391866070447793539124105460668568853618924\

3132905693874616958336079958862242579650280812660512453816275628067977\

7721150419713278365400937039926619418164741229089532498330068239309776\

1690074453198227284210005164670550843915175125291348603192500942129571\

2160296397474642360130036975254240806723286365854612676445799004846266\

7602028680911873106587947193189889293999449715734241944639662748710845\

3864217222758522411029165882690689971923777751749568939373903823332879\

0347862820497821662686301328739580127103593058742239980461079578843089\

8938404770001288892056326897984920834525603021493609403571623845097415\

9269047818150038841906826639724779147047347019045703317553593717846683\

7809250765440348545752291612966122145077943669090956833677756556314535\

3415742755622794040068289994068630691327156047081726660842339291269766\

7917971187981886248629293392246074136458310437500753586451933193176668\

2313587611783431933780044950953903564442478335965847599970260746987255\

0731160508492599759339823308128315559840203913178785278415738419343860\

320599550946803281571941063514234186096009901328/\

5787037037037037037037037037037037037037037037037037037037037037037037\

0370370370370370370370370370370370370370370370370370370370370370370370\

3703703703703703703703703703703703703703703703703703703703703703703009\

2592592592592592592592592592592592592592592592592592592592592592592592\

5925925925925925925925925925925925925925925925925925925925925925925925\

9259259259259259259259259259259259259259259259259259259259259259537037\

0370370370370370370370370370370370370370370370370370370370370370370370\

3703703703703703703703703703703703703703703703703703703703703703703703\

7037037037037037037037037037037037037037037037037037037037037

In[121]:= N[%120]

Out[121]= 1.934431447048015*10^616

]]>Ahh, Crown Sterling again…

Speaking of Kings Crowns and British Sterling.

William Shakespeare in his play Hamlet gave us the phrase,

Which is a common euphemism in the UK[1], and what appears to have happened to Mr Grant…

[1] It implies that “Poetic Justice” or “an ironic reversal of fate on a beligerant” has happened. A Petard[2] is a “breaching bomb” from the time gunpowder was the only real explosive. Basically it was a small iron barrel about 1/3rd full of gunpowder with iron spikes on the outside of the barrel. To use it a grenadier would light the fuse, run up to the wooden doors to be breached and smash it hard against the door so it stuck on the spikes. The grenadier would then beat a vary hasty retreat and would most probably be shot if the petard did not go off very quickly. So the grenadier would cut the fuse as short as he would dare. If he cut it to short then the grenadier is quite literally hoisted off his feet by the explosion, hence the phrase.

[2] Now for the etymology that amuses the inner school boy, we all have but deny 😉 Petard is from the French word “pétard” from the late 16th century. It in turn is from the “Middle French” word péter meaning “break wind,” from Old French word “pet” for “a fart”. I’ve mentioned befor the very expensive late 1980’s sales drive by GEC Plessey Telecomms after they rebranded as “GPT” in France. It goes down in the annals of historic marketing failiures because of an American Marketing Guru who shall remain anonymous. They advised that those giving talks should boldly “own the lectern” by going up and saying their name then GPT to “reinforce the brand”. But importantly with a slight French accent on the GPT to “promote encompassement” (what ever the heck that means 😉 Well if you say “Bill Smith, GPT” with an American idea of what a French accent might be on the GPT, to a Frenchman what he hears in his head is “Bill Smith, I have farted”…

]]>Is seven times, the PNP might affect the equation, but you could sum it down 5/8 of 1 plus 2. ]]>

But my question is why (in general, I am not talking just Crown Sterling) is factoring semi-Primes considered impossible? I think you guys are stuck on the fact that Primes have know patterns. But that is the wrong problem to work on. A patterns in factoring are possible. And those factoring patterns can be applied to semi-Primes. I could argue more put I will give an example:

/* PNPcheck = sqrt[(((((x ^ 2) * (PNP ^ 4) + 2 * PNP ^ 2 * (x ^ 5)) + x ^ 8) / PNP ^ 4) * (((PNP ^ 2) / x ^ 2)))];

```
estimate = (2 * x ^ 5 / PNP ^ 2 + x ^ 8 / PNP ^ 4);
```

*/

```
pnp_check = (((( (x*x) * (PNP*PNP*PNP*PNP) + 2 * (PNP * PNP) * (x*x*x*x*x)) + (x*x*x*x*x*x*x*x)) / (PNP*PNP*PNP*PNP)) * ( ( (PNP*PNP) / (x*x) )));
root = sqrt(double(pnp_check));
```

PNPcheck = n and x = p in n=p*q

You know n and plug in a guess for x. With 2 guess values less than the correct x and a value greater than the correct x, a normal distribution will find the correct x.

This works with factoring all numbers.

So if you continue to use brute force to attack semi-Primes you will be in an endless battle. I can make numbers bigger and you can factoring them, but the process never ends. You find a pattern and create a function and you change the game.

Of course you don’t believe me. So give me advice on how I can multiply a large number by itself 7 times. If you take the time to test the equation you may believe.

]]>They’ve been re-hashing the mod24 quasi-prime wheel for very long time.

Apart from the history Bruce linked above, most information has been in the instagram (go figure):

The prime wheel first appeared in August 7, 2018.

The findings from Shakespeare Sonnets with Alan Green appeared in Sept 29, 2018.

A Picture from March 12 this year shows Grant being interviewed for the Thrive movie https://www.youtube.com/watch?v=lEV5AFFcZ-s — I tried skimming it and the end credits, but didn’t find him anywhere.

March 21 shows him sketching the Time AI logo.

He did the privacy piracy interview, Ted Talk, The prime wheel interview for Hold my Ark. Then there was the blackhat talk, cado-nfs presentation, and now apparently they hosted a new age conference called Conference on Precession of Ancient Knowledge, or, CPAK: https://www.instagram.com/p/B3Cen7WnNo0/?igshid=a4usg3kn0xfu

My guess is Crown Sterling is still in its baby steps.

But if you look at https://www.youtube.com/watch?v=8paZWjiJIk8 you’ll see the company portfolio of Strathspey Crown (the parent company?) and all the snake oil in the world from Audiophile crap, medical patches with hundreds of medications in them, something called GeneRADAR that looks A LOT like the Theranos blood scanner, Botox alternative called Jeuveau, some social media app for physicians, some refrigerant..

And then there’s Torus Tech:

Torus Tech focuses specifically on quantum vacuum energy technologies across a wide area of application including energy production, gravitational control, health and medical treatments and many more. Resonance science and unified physics theory lie at the core of all these applications carried by a strong partnership between our research team and the core engineering team.

They have a product called “Harmonic Flux Resonator”:

Replicating the magnetohydrodynamics occurring in a variety of astrophysical objects.

Energy extracted directly from the vacuum. Nothing to burn, nothing to consume, nothing to destroy. No fumes, no toxins, no limitations. Nothing short of a paradigm shift which will alter the course of human kind forever.

So… free energy… Oh, they have another product:

ARK® crystals are a revolutionary technology that greatly boosts the body’s natural ability to attune with the vitalistic and expansive zero-point field of the quantum vacuum. The quantum vacuum represents the revelatory understanding in modern physics that space is not empty; on the contrary, it is the one thing that connects all things.”

They are serious about selling you $51,200 piece of machined bullshit: https://arkcrystals.com/product/64-ark-crystal-bundle/ (I really like the looks though, maybe it passes as art, at least in their opinion).

My favorite part on that site however is the “this is all bullshit” legal disclaimer they have to put there:

DISCLAIMER – Statements made on this site have not been evaluated by the Food and Drug Administration. This product is not intended to diagnose, treat, cure, or prevent any disease. Consult your own doctor.

So, with that being said, considering Time AI is the last item on that portfolio, it could also be the newest. The reason Crown Sterling hasn’t done anything else yet is because they’ve been really busy building an empire of bullshit.

I’m fairly sure these guys will make the main story on John Oliver by the end of the next decade.

]]>You’ve been having fun 😉

I’ll have a more detailed think about it but my gut instinct on first reading is you are right.

Mind you appart from the initial flurry of ruffled feathers from Crown Sterling news wise the story appears to have sunk without trace.

@ ALL,

Does anyone know if Crown Sterling has done anything other than their initial bluster reported in the news?

]]>In the previous post I tried to evaluate the efficiency of the Crown Sterling reciprocal factoring method. Turns out there is no memory requirement for it. But it’s still not feasible:

Looking at https://www.geeksforgeeks.org/find-length-period-decimal-value-1n/ the way the algorithm

def getPeriod(n) : # Find the (n+1)th remainder after decimal point in value of 1/n rem = 1 # Initialize remainder for i in range(1, n + 2): rem = (10 * rem) % n # Store (n+1)th remainder d = rem # Count the number of remainders before # next occurrence of (n+1)'th remainder 'd' count = 0 rem = (10 * rem) % n count += 1 while rem != d : rem = (10 * rem) % n count += 1 return count

produces the period, is it first iterates over the range (1, n+2), so the first step has n+1 steps.

The remainder is then stored, and remainders are iterated backwards until the remainder repeats: the second part only requires as many steps as the period has length.

So, for RSA-2048, you need 2^{2048} + len(period) steps to determine the period.

The most efficient way to find the factors is, while you’re iterating over the 2^{2048}+1 steps, you keep log_{10}sqrt(2^{2048}) digits long substring (308 for RSA 2048) that is the RSA prime factor candidate (best case scenario).

When you produce the next decimal with the algorithm above, you need to slice off from the other end in order to prevent the memory cost from reaching insane levels: Like I said in the previous post, for just the RSA-100 (that has been insecure since the 80s) you’d have to store 15226050279225333605356183781326374297180681149613

80688657908494580122963258952897654000350692006139-1 digits, i.e. **you’d have to store in the order of 10 petabytes of digits inside every atom in the observable universe**.

Once you’ve added the next decimal of the reciprocal to the substring, you have 309 digit long substring. Thus, you have to slice one digit from the other end to get back to the 308 digit substring. This substring is most likely not prime, but checking that with a really efficient test like Rabin-Miller takes much much longer than just seeing whether it divides the semi-prime evenly. So to see if the substring is a prime factor, you just divide the semi-prime with it.

Because you sliced the one digit from the other end after every iteration, you have to keep doing the division after every step, because otherwise you might miss the prime factor candidate.

The question is, how efficient is this?

Well, I took time to implement as efficient algorithm as I could based on the non-existent documentation (read: the instagram post) with Python (the language should matter very little as we’re comparing efficiency between the algorithms by counting the steps, not by comparing the execution time).

The source code along with example output can be found here: https://gist.github.com/maqp/b04e27e795ab01c5cdefdcddc59e3a02

**The tl;dr is, for that particular game of 100 rounds with 32-bit semiprimes, the Crown Sterling Reciprocal Factoring Method was on average 5.85 times slower than random division (brute force).**

Note that the implementation of the reciprocal factoring method we’re using does not first have to iterate over the entire reciprocal, it’s testing the period on the fly so it exits as soon as possible.

Considering the comparison, it can be concluded the reciprocal factoring algorithm is just a crappier implementation of trial division, and that both run in exponential time (which in turn means **Crown Sterling has achieved nothing**.)

This makes it a lot less efficient than GNFS of the cado-nfs program they were using to break RSA256, and as shown above, slower than brute force.

While I’ve been thinking about this, I asked the good folks at cryptography.stackexchange.com about Crown Sterling’s reciprocal factoring method:

The top answer turned out to be a fascinating read and technical dissection of the snake oil claims by the company. I highly recommend reading it.

]]>