Block #143,314

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/31/2013, 1:52:55 PM · Difficulty 9.8373 · 6,663,243 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

68be571e00e99d2bf969fcd146973d4a1e883a2cf78e2eb76eaa7d87b593a7c0

View on Chainz ↗

Height

#143,314

Difficulty

9.837259

Transactions

Size

356 B

Version

Bits

09d6569c

Nonce

205,309

Timestamp

8/31/2013, 1:52:55 PM

Confirmations

6,663,243

Mined by

⛏️ P2SHANkSBqbEXP5SFNG3bGPJ6iV1UsLajBMwP7

Merkle Root

54c80762208905535837a180fe46c6a877b85283c89a1b21ac749952bd89bdbf

Transactions (2)

Coinbase8012ab088d702d…05dfe3cf967669

1 in → 1 out10.3300 XPM109 B

ANkSBqbE…LajBMwP7

f7b82f4c3504a9…9eac3a0675223c

1 in → 1 out10.3600 XPM158 B

AQg4a2bg…GPv4ag9L

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.

3.875 × 10⁹¹(92-digit number)

38759169308485287586…85150505541781747199

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

3.875 × 10⁹¹(92-digit number)

38759169308485287586…85150505541781747199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.875 × 10⁹¹(92-digit number)

38759169308485287586…85150505541781747201

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

7.751 × 10⁹¹(92-digit number)

77518338616970575173…70301011083563494399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.751 × 10⁹¹(92-digit number)

77518338616970575173…70301011083563494401

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

1.550 × 10⁹²(93-digit number)

15503667723394115034…40602022167126988799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.550 × 10⁹²(93-digit number)

15503667723394115034…40602022167126988801

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

3.100 × 10⁹²(93-digit number)

31007335446788230069…81204044334253977599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.100 × 10⁹²(93-digit number)

31007335446788230069…81204044334253977601

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

6.201 × 10⁹²(93-digit number)

62014670893576460138…62408088668507955199

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 #143,314

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