One of the numbers is not prime and the second number is the number that needs to be tested for primality. "Prime1" = 35 Prime2 = 97 They can't equal each other. Data1 = 1 Data2 = 2 Calculate MMI MMI1 = Prime2 ^ -1 Mod Prime1 MMI2 = Prime1 ^ -1 Mod Prime2 For Prime Numbers only (it will give a number for non-prime numbers but it won't be its MMI): MMI1 = (Prime2 ^ (Prime1-2))% Prime1 MMI2 = (Prime1 ^ (Prime2-2))% Prime2 e.g MMI1 = (97 ^ 33)% 35 MMI2 = (35 ^ 95)% 97 For MMI1 F(1) = Prime2% Prime1 = 97% 35 = 27 F(2) = F(1) * F(1)% Prime1 = 27 * 27% 35 = 29 F(4) = F(2) * F(2)% Prime1 = 29 * 29% 35 = 1 F(8) = F(4) * F(4)% Prime1 = 1 * 1% 35 = 1 F(16) =F(8) * F(8)% Prime1 = 1 * 1% 35 = 1 F(32) =F(16) * F(16)% Prime1 = 1 * 1% 35 = 1 Calculate the binary of Prime1 - 2 35 -2 = 33 (10001) base 2 MMI1 = F(33) = F(32) * F(1) mod 35 MMI1 = F(33) = 1 * 27 Mod 35 MMI1 = 27 For MMI2 F(1) = Prime1% Prime2 = 35% 97 = 35 F(2) = F(1) * F(1)% Prime2 = 35 * 35 mod 97 = 61 F(4) = F(2) * F(2)% Prime2 = 61 * 61 mod 97 = 35 F(8) = F(4) * F(4)% Prime2 = 35 * 35 mod 97 = 61 F(16) = F(8) * F(8)% Prime2 = 61 * 61 mod 97 = 35 F(32) = F(16) * F(16)% Prime2 = 35 * 35 mod 97 = 61 F(64) = F(32) * F(32)% Prime2 = 61 * 61 mod 97 = 35 F(128) = F(64) * F(64)% Prime2 = 35 * 35 mod 97 = 61 Calculate the binary of Prime2 - 2 97 - 2 = 95 = (1011111) base 2 MMI2 = (((((F(64) * F(16)% 97) * F(8)% 97) * F(4)% 97) * F(2)% 97) * F(1)% 97) MMI2 = (((((35 * 35) %97) * 61)% 97) * 35% 97) * 61% 97) * 35% 97) MMI2 = 61 Answer = (1 * 97 * 27 + 2 * 35 * 61)% (97 * 35) Answer = (2619 + 4270)% 3395 Answer = 99 Calculate (Answer - Data1)% Prime1 99 -1% 35 = 28 Since 28 is greater than 0, 35 is not prime Calculate (Answer - Data2)% Prime2 99 - 2% 97 = 0 Since 0 equals 0, 97 is potentially prime If step 7 is 0: Use a different "prime1" where prime1 is a non-prime Use a different prime 1 where prime 1 is an actual prime. In this case, steps 6 and 7 should equal 0. Use different data points for data1 and data2. If step 7 is 0 every time, there is an extremely high probability that prime2 is prime. Steps 1 though 7 are known to fail in certain cases when the first number is a non-prime number and the second prime is a factor of the non-prime number "prime1". It works in all scenarios where both numbers are prime. The reason why steps 1 though 7 are repeated is because there are a few scenarios where, even if prime1 is not prime and prime2 is not prime, step 7 still works out to be zero, for one or both the numbers. These circumstances are rare. By changing prime1 to a different non-prime number, if prime2 is not prime, prime2 will rapidly not equal zero in step 7. Except for the instance where "prime1" is a factor of prime2, prime numbers will always equal zero in step 7.
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One-sentence summary -- Choose two numbers. Choose two datapoints that are greater than zero and less than prime1 and prime2 respectfully. Calculate MMI (Mathematical Multiplicative Inverse) for Prime1 and Prime2 Create a binary table for each MMI up to Log2 of the Modulus Calculate (Data1 * Prime2 * MMI1 + Data2 * Prime1 * MMI2)% (Prime1 * Prime2) Verify that "Prime1" is not Prime Check if Prime2 is Prime Repeat steps 1 through 7 at least two more times.

Using a warm, wet cloth, take a few passes at the spot to get the worst of the mess out of the way. Because of the way carpet and fabric upholstery are made, much of the droppings will collect and harden at the top of the fibers, making the bulk of it easier to wipe away. Use pinching, pulling motions with the wet cloth to coax the droppings out of the carpet or upholstery. Depending on exactly what type of surface you're cleaning and what materials it's made of, you'll want to purchase some special cleaner that is guaranteed to work safely on that surface. Most standard carpet cleaners or all-purpose household cleaners will be mild enough to work on any kind of carpet, and foaming upholstery cleaners can be found at any supermarket or drugstore. Spray enough cleaner onto the spot to cover what's left of it. If you do not have any specialized carpet cleaner on hand, you also have the option of mixing up a gentle solution consisting of mild laundry detergent, vinegar and warm water. Give the cleaner two or three minutes to sit on the spot. The chemical compounds in the cleaner will begin to eat away the hardened stain, making it easy to wipe away later. Use a damp washcloth to go over the spot once again. The stain-fighting power of the cleaner combined with the force of scrubbing by hand should be enough to take the spot out of your carpet or upholstery. If any traces are left after scrubbing, spray a little more cleaner on the spot, let it sit, then make a second attempt. Scrub forcefully to ensure that you get as much of the dried-on mess out of the deeper layers of the carpet as you can. Always wash any washcloth or towel that comes into contact with bird poop right away.
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One-sentence summary --
Give the spot an initial go-over. Spray on some upholstery care or carpet cleaner. Let the cleaner start to work on the spot. Wipe away the remaining mess.