Block #313,314

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/15/2013, 10:11:35 AM · Difficulty 9.9961 · 6,483,512 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

471624509dc19923ef0f33571ee5b0f3bcfa13d9f2efde2ab0018ccedc915d6d

View on Chainz ↗

Height

#313,314

Difficulty

9.996083

Transactions

Size

1.77 KB

Version

Bits

09feff44

Nonce

4,799

Timestamp

12/15/2013, 10:11:35 AM

Confirmations

6,483,512

Mined by

⛏️ aR_Ad9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

6ea20920d443528f55e2e8e2849c63777a2cdf03a7dc08500171a064d3a56b90

Transactions (4)

Coinbase64d856a3988b5a…bfdaf2ff0d8efc

1 in → 29 out9.9700 XPM1.02 KB

Ad9pSzHt…cpJ3y2zz Aac9Hjdg…P4ktypc3 AG5YAjec…VhA4Aeh1 APeshfYV…3PKcKMKH ARy21REr…6pBWtQJ2

4ae3d95b355064…9fa9aff90e2bc2

1 in → 2 out5.9571 XPM225 B

AGgraJCm…RK4cKNoT AWNTU5FN…WsVFrQ51

e1da4c83926236…8c34d25c7c186a

1 in → 2 out4.6545 XPM227 B

AZQbyKCf…J2MYYwBM AcQfxVUD…vQnNph4X

f5bdb329df80af…f65f4a6397adf5

1 in → 2 out5.3873 XPM227 B

AV1fcUkn…pr2f7hqH ALxRBCwR…ExA5ijBj

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.

2.875 × 10⁹¹(92-digit number)

28754169863857770055…49272296627131494399

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

2.875 × 10⁹¹(92-digit number)

28754169863857770055…49272296627131494399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.875 × 10⁹¹(92-digit number)

28754169863857770055…49272296627131494401

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

5.750 × 10⁹¹(92-digit number)

57508339727715540111…98544593254262988799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.750 × 10⁹¹(92-digit number)

57508339727715540111…98544593254262988801

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

1.150 × 10⁹²(93-digit number)

11501667945543108022…97089186508525977599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.150 × 10⁹²(93-digit number)

11501667945543108022…97089186508525977601

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

2.300 × 10⁹²(93-digit number)

23003335891086216044…94178373017051955199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.300 × 10⁹²(93-digit number)

23003335891086216044…94178373017051955201

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

4.600 × 10⁹²(93-digit number)

46006671782172432089…88356746034103910399

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