Block #382,740

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/30/2014, 10:46:48 PM · Difficulty 10.3996 · 6,443,759 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ca950c7b20ab9c554c97c96829da64595cc31c4f4f426f6eab8ade902148f0ff

View on Chainz ↗

Height

#382,740

Difficulty

10.399598

Transactions

Size

660 B

Version

Bits

0a664c12

Nonce

3,338

Timestamp

1/30/2014, 10:46:48 PM

Confirmations

6,443,759

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a58c25dec9bb50efa42e713a2d5fd34180321744dc3551d26461c8da7d90ef3c

Transactions (3)

Coinbaseb106e24286e019…f912802d1bb8a9

1 in → 1 out9.2500 XPM116 B

AbwWkWZt…kawDhufa

0bcf239dfe3bb4…6992bc6f451a9c

1 in → 2 out8.1799 XPM227 B

AXxp24rY…yi3yUFBu ALxxKq1k…QGaga481

2100b93ba213d0…3049ef0d55a821

1 in → 2 out7.1692 XPM227 B

AVD7e7bi…wDAsvwk4 AWt82SkA…ap2AjpsW

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.

3.773 × 10⁹⁴(95-digit number)

37730049595483597441…87913782545636796159

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

3.773 × 10⁹⁴(95-digit number)

37730049595483597441…87913782545636796159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.773 × 10⁹⁴(95-digit number)

37730049595483597441…87913782545636796161

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

7.546 × 10⁹⁴(95-digit number)

75460099190967194883…75827565091273592319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.546 × 10⁹⁴(95-digit number)

75460099190967194883…75827565091273592321

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

1.509 × 10⁹⁵(96-digit number)

15092019838193438976…51655130182547184639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.509 × 10⁹⁵(96-digit number)

15092019838193438976…51655130182547184641

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

3.018 × 10⁹⁵(96-digit number)

30184039676386877953…03310260365094369279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.018 × 10⁹⁵(96-digit number)

30184039676386877953…03310260365094369281

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

6.036 × 10⁹⁵(96-digit number)

60368079352773755906…06620520730188738559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.036 × 10⁹⁵(96-digit number)

60368079352773755906…06620520730188738561

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 #382,740

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