Block #306,578

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 3:05:44 AM · Difficulty 9.9939 · 6,502,882 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8804d96f080ee7f87b346bf281aa3664c238d881bb441bbbd722272ca1f3a4ae

View on Chainz ↗

Height

#306,578

Difficulty

9.993932

Transactions

Size

1.45 KB

Version

Bits

09fe7252

Nonce

2,486

Timestamp

12/12/2013, 3:05:44 AM

Confirmations

6,502,882

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

5b5f3ff25be3dd20cf4db4751e26de5769cfbf74279cc9cc1b65029ddc584b30

Transactions (3)

Coinbasecf9429ea391a98…005106c7e5fd19

1 in → 1 out10.0200 XPM110 B

AeKNrjNj…1NEq95Ta

a896f1b9346747…412fbdfb7d53d2

4 in → 13 out40.1800 XPM908 B

ANXdjzRU…S2ppC19z AXdvskLG…hn79o8Av AXq1FUZY…39C33und Abu1uzTT…6jPtvXzW AeKNrjNj…1NEq95Ta

2a2a128e7e953b…631ba4856b06ef

2 in → 2 out1.3885 XPM374 B

AWuMk4BD…8c5hmrC1 AZ3bxBs6…Xt3Wo7nv

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.

4.972 × 10⁹¹(92-digit number)

49720446744694917900…98917881380693458559

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

4.972 × 10⁹¹(92-digit number)

49720446744694917900…98917881380693458559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.972 × 10⁹¹(92-digit number)

49720446744694917900…98917881380693458561

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

9.944 × 10⁹¹(92-digit number)

99440893489389835800…97835762761386917119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.944 × 10⁹¹(92-digit number)

99440893489389835800…97835762761386917121

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

1.988 × 10⁹²(93-digit number)

19888178697877967160…95671525522773834239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.988 × 10⁹²(93-digit number)

19888178697877967160…95671525522773834241

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

3.977 × 10⁹²(93-digit number)

39776357395755934320…91343051045547668479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.977 × 10⁹²(93-digit number)

39776357395755934320…91343051045547668481

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

7.955 × 10⁹²(93-digit number)

79552714791511868640…82686102091095336959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.955 × 10⁹²(93-digit number)

79552714791511868640…82686102091095336961

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #306,578

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