Block #383,193

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/31/2014, 6:40:46 AM · Difficulty 10.3979 · 6,426,219 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

55144fdbd33c5155c481904bacba43cfbbc5977d8d2def80a2b60de064f295bb

View on Chainz ↗

Height

#383,193

Difficulty

10.397856

Transactions

Size

1.41 KB

Version

Bits

0a65d9de

Nonce

6,355

Timestamp

1/31/2014, 6:40:46 AM

Confirmations

6,426,219

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

17c0a422f8b4cc249890cde68feff909e5e1662a8253ad9be45209cf14785793

Transactions (2)

Coinbased9521105de5bea…dc115383b0af2c

1 in → 1 out9.2600 XPM116 B

AbwWkWZt…kawDhufa

381ed6a6cae770…c4aefcc6436539

6 in → 15 out46.5885 XPM1.21 KB

ARtQNNRy…toP7whAT AdiFFru7…NxkvJkLD AZJ31Mao…gCve1AhC AJTnJPkG…6HTSvS8F AJyGidYK…wD9VP2WE

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.

4.505 × 10⁹⁵(96-digit number)

45057135849390916578…55782329015497162239

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

4.505 × 10⁹⁵(96-digit number)

45057135849390916578…55782329015497162239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.505 × 10⁹⁵(96-digit number)

45057135849390916578…55782329015497162241

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

9.011 × 10⁹⁵(96-digit number)

90114271698781833156…11564658030994324479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.011 × 10⁹⁵(96-digit number)

90114271698781833156…11564658030994324481

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

1.802 × 10⁹⁶(97-digit number)

18022854339756366631…23129316061988648959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.802 × 10⁹⁶(97-digit number)

18022854339756366631…23129316061988648961

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

3.604 × 10⁹⁶(97-digit number)

36045708679512733262…46258632123977297919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.604 × 10⁹⁶(97-digit number)

36045708679512733262…46258632123977297921

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

7.209 × 10⁹⁶(97-digit number)

72091417359025466524…92517264247954595839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.209 × 10⁹⁶(97-digit number)

72091417359025466524…92517264247954595841

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 #383,193

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