Block #377,936

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/27/2014, 11:36:26 AM · Difficulty 10.4203 · 6,438,656 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

26712335c72cbbedc9e20dd0906214479c6a859e40d4dad66ed3d6992274e459

View on Chainz ↗

Height

#377,936

Difficulty

10.420321

Transactions

Size

1.19 KB

Version

Bits

0a6b9a2f

Nonce

730,418

Timestamp

1/27/2014, 11:36:26 AM

Confirmations

6,438,656

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

352a9bd16bb0905744818527eeb10ac8f4335ecd404a6b9050d65654e3e758ac

Transactions (4)

Coinbaseae5d592ee67e73…9eaaf685b401d7

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

c605bc09267bc8…7114126009bc03

2 in → 1 out500.0000 XPM338 B

AZD5zWVk…WaHRqp5F

719cef29e5b9f2…b8dbb9f25a5c4a

3 in → 1 out361.2900 XPM489 B

Aej9kddU…caLti9Dv

14701b71b46e17…6c5698ef31488a

1 in → 1 out79.9900 XPM192 B

AdJ2RAaa…qRJTXpp7

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.

7.199 × 10¹⁰²(103-digit number)

71994288933725790883…52633584456894630559

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

7.199 × 10¹⁰²(103-digit number)

71994288933725790883…52633584456894630559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.199 × 10¹⁰²(103-digit number)

71994288933725790883…52633584456894630561

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

1.439 × 10¹⁰³(104-digit number)

14398857786745158176…05267168913789261119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.439 × 10¹⁰³(104-digit number)

14398857786745158176…05267168913789261121

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

2.879 × 10¹⁰³(104-digit number)

28797715573490316353…10534337827578522239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.879 × 10¹⁰³(104-digit number)

28797715573490316353…10534337827578522241

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

5.759 × 10¹⁰³(104-digit number)

57595431146980632706…21068675655157044479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.759 × 10¹⁰³(104-digit number)

57595431146980632706…21068675655157044481

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

1.151 × 10¹⁰⁴(105-digit number)

11519086229396126541…42137351310314088959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.151 × 10¹⁰⁴(105-digit number)

11519086229396126541…42137351310314088961

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 #377,936

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