General rules for Krishna Software's equations: we generally write equations that are in integer domain or preferably in the natural number domain so there are no decimal points and results are 0...infinity (no negative numbers). All the equations involving lucky 7 are lossless meaning even if they involve intermediary non-integer calculations, fractions are used so nothing is lost in the next calculation. For example, one of Lovely's lucky7 composite (LLC) equation is: L(n+1) = 7*L(n)+5/7 with L(0)=1. If we used the decimal form of 5/7, we end up trying to keep infinite digits since 5/7 = 0.7142857142857... Also, in LORE (Lovely's Original Remainder Equation), where we divide the numbers and keep only the remainder R(n+1), nothing is lost since the remainder is always a positive integer as long as we set our initial condition R(0) to a positive integer (R(0)>0). Even our date calculations where m=month, d=day, and y=year, we try to use only addition, multiplication, certain quotients w/remainders, just remainders, and certain powers of positive whole numbers (integers). There are no multipliers for m, d, and y or other constants added to m, d, and y other than those allowed for or given in the original problem. This is what we call Simple Positive Analysis (SPA). By default for date analysis, only multiplier and/or constant allowed is 7 since that's related to days in a week, planets, and our lucky number for positive influence. Therefore all calculations of SPA are all positive whether doing intermediary calculations or in the final result. The result should simply flow out easily from the equation and not involve complicated calculations. For example, 10/25/2023, sum of month and day is 35 (m+d = 35 = 7*5). Sum of m+d+y = 2058 = 2*3*7^3. Here 7^3 means 7 to the power of 3 or 7*7*7 or 7 cubed. Remainder of y/(m+d) = 28 or 7*4. If we involved negative numbers, complex quotients, arbitrary constants multiplying the month, day, or year other than those allowed for like 7, etc. then it's a complex integer analysis (CIA). Obvioulsy, if you used decimal points and real numbers you can get any resultant value from the f(m,d,y). But time in the universe is only a positive entity and there is quantization of days, hours, etc. in reality corresponding to planets, the sun, and other things not something arbitrary defined. To prove the rarity of "lucky 7", SPA is used and if SPA cannot generate our lucky 7 then we have no choice but concede that lucky 7 is not meant for that day. A glossary of acronyms used by Krishna Software Inc. is given at the end of this article (not an exhaustive list but enough for this article). Vpp Equations (Virender's prime to prime equations)-- [documentation is incomplete] In layman's terms, if you have ever tried to cross a small shallow river or stream in the forest and did not want to get dirty or you didn't want to get wet, you usually try to find areas in the river where there are rocks that stick out of the water that you can step on until you can cross. In this analogy the rocks sticking out of the water are the prime numbers and presumption is that the water level of the stream/river is constant (does not change). Just as in crossing the river you step on one rock after another that is not submerged in the water so Vpp equation is an equation that goes from one prime to another as far as possible without running into a composite number... We are not trying to exhaustively get all the primes to fit into our equation just like in crossing the river we are not trying to find all the rocks that are above the water. Initial condition of the equation is given in P(0). For versions of the equation that require two initial conditions, then P(1) would become the first initial condition and P(0) becomes the second initial condition. For three initial conditions, P(2) is the first initial condition, P(1) is the second initial condition, and P(0) is the third initial condition. And so on. Initial conditions do not have to be primes just like when crossing the river you can start on one bank of the river that does not necessarily have to be a rock not submerged in the water. For example, P(0)=lg(3) is an example of an initial condition that works fine for generating prime numbers for one of our Vpp equations. P(n) = f(P(n-1)) as n goes from 1 and up. Obviously, in this example, P(0) is neither prime nor composite since lg(3) = 1.5849625... Here "lg" means logarithm of base 2 so lg(2048)=11 whereas log(x) means base 10 logarithm so log(1000)=3 and ln(x)=logarithm to the base e which is an irrational constant (e=2.718281828459045... or to be more exact, e=SUM(1/n!) (n=0..infinity). In trying to come up with this equation (Vpp) I did come up with several equations that work for generating consecutive primes for a certain range. Let us start with an easy example that works in generating a limited number of consecutive prime numbers: P(n+2) = 2*P(n-1)-P(n)+2. If we let the difference between two recently generated primes be delta P; i.e., dP = P(n-1)-P(n) then this equation becomes P(n+2) = P(n-1)+dP+2. If you didn't recognize this equation, that's the same equation we derived in another article for perfect squares with initial conditions of P(0)=4 and P(1)=1. We just have to modify the two initial conditions P(1) and P(0) to start generating primes. If we let P(0)=P(1)=17 (Q) then we can generate 16 (Q-1) consecutive primes in range of [Q..Q*Q]. Similarly, if we let P(0)=P(1)=41 then we can generate 40 (41-1) consecutive primes in range of [41..41*41]. To be continued... ------------------------------------------------- Glossary 7-OLOGY = the study of 7, its close relatives like 17 and 119, and remote relatives like 24 (17+7), 41 (17+7+17), etc. ANTIC = apparently not taught in colleges. CIA = complex integer analysis. HPX = Hokey Pokey Xform (transform) where the digits of a number are rotated about its center derived from "put your right number in, put your left number out, do the hokey-pokey and turn your numbers around; that's what it's all about." For example, HPX(911)=119 and for any number with power (exponent), HPX(a^p)=p^x. To make HPX(x) complete, the inverse function would have to be defined and in our case HPX(x) has an inverse function which is HPX(x) itself; i.e, HPX(HPX(x))=x. There are bit more details to this like derivative and integration where the constant is lost in taking the derivative and must be accounted for when integrating to complete the inverse. IRS = individual recursive sum: when digits are summed up in a number or numbers independently of their weights. IPAD = interest in profit, adoration, and distinction. L7L = Lovely's 7th Law of math: a proven fact that if given integers i,j, and k, if i%k=0 and j%k=0, then (i+j)%k = 0 and (i*j)%k = 0.
LLC = Lovely's Lucky7 Call: a type of equation that generates values containing infinite multiples of 7 but involves fractions. LOG(f(d)) = A deductive positive function f(d) derived due to love of God or "luck" of God helping you (divine intervention). If f(d) you came up with is unrelated to all the hard work and research you did and is better than the function you derived then the credit you should get is log(f(d))/f(d). Any function you get due to love is greater than any function you can get with all the money and knowledge in the world; i.e., L>=m*k*k or love is greater than or equal to money times knowledge squared. LORE = Lovely's Original Remainder Equation: a type of recursive equation that extracts remainders of division based on previous remainder. The input and output of this equation is always a positive integer and initial condition of R(0) is usually the month (mm) and day (dd) in either mm+dd or mmdd format where mmdd is equivalent to mm*100+dd. SLIP = Simply Lovely's Inverse Pi: scaled version of 1/pi where the scale is fixed at 10^16. This yields 16-digit integer 3183098861837906. If the scale is other than 10^16 then it must be explicitly specified in the parentheses like SLIP(10^32). Note that to get queen size integer for the inverse of pi, scale factor of 10^17 is needed and this is given by SLIP(10^Q) where Q=17 or queen size. SPA = simple positive analysis -- a type of integer analysis using only addition, multiplication, remainders, and powers of positive numbers and any given positive constants. SPY = Scaled Pi Yields: when pi is scaled by 10^16 then the integer it yields is SPY. If the scale is other than 10^16 then it must be explicitly specified in the parentheses like SPY(10^27). By default SPY() or just SPY refers to scale of 10^16 which has been found to contain a gold-mine of 7s in various forms and used in study of 7-ology.