Block #374,986

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/25/2014, 10:26:24 AM · Difficulty 10.4196 · 6,455,474 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

963f5759089380bd7e0ca5e73f7d67c26d1cfd4df00ccaa4b3f8bb64b39ea062

View on Chainz ↗

Height

#374,986

Difficulty

10.419592

Transactions

Size

1.05 KB

Version

Bits

0a6b6a62

Nonce

12,450

Timestamp

1/25/2014, 10:26:24 AM

Confirmations

6,455,474

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

618774d3b8bf16f7d88a912ec0b262d433e3115e80a84d07d0b96c37e6e784ab

Transactions (2)

Coinbasebd8986339c981b…b6b14f66f38184

1 in → 1 out9.2100 XPM110 B

AeKNrjNj…1NEq95Ta

c28e13ec33bfa9…529b93f1f96284

4 in → 12 out36.8000 XPM873 B

AN3r4D36…jEiyTM3F AYZKwCtP…SDKpV9DS AMMXZMYS…CndbCJe9 AT1J5EU6…DXMqPCZD AVkzgzs3…UR81BPTx

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.

1.510 × 10¹⁰⁴(105-digit number)

15106243638729553587…14392608631977121279

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

1.510 × 10¹⁰⁴(105-digit number)

15106243638729553587…14392608631977121279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.510 × 10¹⁰⁴(105-digit number)

15106243638729553587…14392608631977121281

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

3.021 × 10¹⁰⁴(105-digit number)

30212487277459107174…28785217263954242559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.021 × 10¹⁰⁴(105-digit number)

30212487277459107174…28785217263954242561

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

6.042 × 10¹⁰⁴(105-digit number)

60424974554918214349…57570434527908485119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.042 × 10¹⁰⁴(105-digit number)

60424974554918214349…57570434527908485121

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

1.208 × 10¹⁰⁵(106-digit number)

12084994910983642869…15140869055816970239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.208 × 10¹⁰⁵(106-digit number)

12084994910983642869…15140869055816970241

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

2.416 × 10¹⁰⁵(106-digit number)

24169989821967285739…30281738111633940479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.416 × 10¹⁰⁵(106-digit number)

24169989821967285739…30281738111633940481

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 #374,986

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