Block #182,370

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/27/2013, 6:13:56 AM · Difficulty 9.8587 · 6,627,737 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a8838bb3f7d17ae67474b3d3de51231e60af81f0eeb79fded6ab3de0a8f8994b

View on Chainz ↗

Height

#182,370

Difficulty

9.858697

Transactions

Size

1.16 KB

Version

Bits

09dbd396

Nonce

3,444

Timestamp

9/27/2013, 6:13:56 AM

Confirmations

6,627,737

Mined by

⛏️ P2SHAWbQMT1UFX9Fb1nejhFo5DMbcK8Pt4ow7J

Merkle Root

d5651df80c63830b229f2665ce9de03e03354a2d7c38df37eb8775e5cbd94e51

Transactions (4)

Coinbase39412e63d4959e…aa56add58a88d2

1 in → 1 out10.3000 XPM109 B

AWbQMT1U…8Pt4ow7J

d140c67cdc470d…ae3a6568bb6e22

3 in → 1 out30.7800 XPM387 B

AMm2NR1w…19uBFzE6

b5337423a3d278…f2114d91649d8d

2 in → 2 out13.2718 XPM373 B

AYS1abVB…jKEPGGsF ALpthvGg…D1g5z4CT

fa2dfd6562d0f2…39d57d7dbb879c

1 in → 2 out8.2340 XPM226 B

APCd5xLU…LN7JeMdv ALfQuJHC…S4MvAE5Q

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.

1.899 × 10⁹⁸(99-digit number)

18994714035158256495…78472542800602594559

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

1.899 × 10⁹⁸(99-digit number)

18994714035158256495…78472542800602594559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.899 × 10⁹⁸(99-digit number)

18994714035158256495…78472542800602594561

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

3.798 × 10⁹⁸(99-digit number)

37989428070316512990…56945085601205189119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.798 × 10⁹⁸(99-digit number)

37989428070316512990…56945085601205189121

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

7.597 × 10⁹⁸(99-digit number)

75978856140633025980…13890171202410378239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.597 × 10⁹⁸(99-digit number)

75978856140633025980…13890171202410378241

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

1.519 × 10⁹⁹(100-digit number)

15195771228126605196…27780342404820756479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.519 × 10⁹⁹(100-digit number)

15195771228126605196…27780342404820756481

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

3.039 × 10⁹⁹(100-digit number)

30391542456253210392…55560684809641512959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #182,370

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