Block #2,818,380

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/31/2018, 11:56:17 AM · Difficulty 11.6982 · 4,026,826 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

5f6648b990af4796feaddcb001111e4d73397c3fc3a6d5d744cba316a929e437

View on Chainz ↗

Height

#2,818,380

Difficulty

11.698172

Transactions

Size

1.61 KB

Version

Bits

0bb2bb66

Nonce

255,103,729

Timestamp

8/31/2018, 11:56:17 AM

Confirmations

4,026,826

Mined by

⛏️ P2SHAQULXX7XGQCE12qPCNdUqrtm5Pv9bUCVci

Merkle Root

b3f0a124e59bda2b3c1dea7aebc3df7493e6f0b787c6b983d5282189f0481c88

Transactions (3)

Coinbase1a95c95e227fac…c1820c66e5985b

1 in → 1 out7.3200 XPM110 B

AQULXX7X…v9bUCVci

4dc36e2b795b4b…f89a70163f8578

6 in → 2 out10.0766 XPM931 B

AdfpiAcF…kbxn7piR ALdXNNLi…KbXoShEJ

07fe046696bc74…a3812bc5084b89

3 in → 2 out4.0325 XPM521 B

AWaYC9BA…1BzTFe5J ANP5uvEM…WztHHDsH

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.988 × 10⁹⁵(96-digit number)

19880926894281738181…36982084453232330239

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.988 × 10⁹⁵(96-digit number)

19880926894281738181…36982084453232330239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.988 × 10⁹⁵(96-digit number)

19880926894281738181…36982084453232330241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

3.976 × 10⁹⁵(96-digit number)

39761853788563476363…73964168906464660479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.976 × 10⁹⁵(96-digit number)

39761853788563476363…73964168906464660481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

7.952 × 10⁹⁵(96-digit number)

79523707577126952726…47928337812929320959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.952 × 10⁹⁵(96-digit number)

79523707577126952726…47928337812929320961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.590 × 10⁹⁶(97-digit number)

15904741515425390545…95856675625858641919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.590 × 10⁹⁶(97-digit number)

15904741515425390545…95856675625858641921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.180 × 10⁹⁶(97-digit number)

31809483030850781090…91713351251717283839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.180 × 10⁹⁶(97-digit number)

31809483030850781090…91713351251717283841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

6.361 × 10⁹⁶(97-digit number)

63618966061701562181…83426702503434567679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,818,380

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