Block #365,880

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/19/2014, 1:40:39 AM · Difficulty 10.4240 · 6,444,834 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

56a7f78d27d2e3ece3450a12c181e3a51a005f6760775728e2aceb6f99914b28

View on Chainz ↗

Height

#365,880

Difficulty

10.424037

Transactions

Size

8.52 KB

Version

Bits

0a6c8daa

Nonce

136,997

Timestamp

1/19/2014, 1:40:39 AM

Confirmations

6,444,834

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

dafbc2b4132cd738dc0267fb330c09130c31d34b78b2ec47f20c15198a1c34ad

Transactions (2)

Coinbasee583bc943367f5…3f21799c61020b

1 in → 1 out9.2800 XPM110 B

AeKNrjNj…1NEq95Ta

380d007e48fffe…a258e0b42d036c

57 in → 2 out99.9118 XPM8.32 KB

AKcxYAr3…mHB3gUCQ AWZse3Gw…haZYm7L8

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.

5.143 × 10¹⁰²(103-digit number)

51432178123305868553…30603681586117340159

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

5.143 × 10¹⁰²(103-digit number)

51432178123305868553…30603681586117340159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.143 × 10¹⁰²(103-digit number)

51432178123305868553…30603681586117340161

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

1.028 × 10¹⁰³(104-digit number)

10286435624661173710…61207363172234680319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.028 × 10¹⁰³(104-digit number)

10286435624661173710…61207363172234680321

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

2.057 × 10¹⁰³(104-digit number)

20572871249322347421…22414726344469360639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.057 × 10¹⁰³(104-digit number)

20572871249322347421…22414726344469360641

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

4.114 × 10¹⁰³(104-digit number)

41145742498644694842…44829452688938721279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.114 × 10¹⁰³(104-digit number)

41145742498644694842…44829452688938721281

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

8.229 × 10¹⁰³(104-digit number)

82291484997289389685…89658905377877442559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.229 × 10¹⁰³(104-digit number)

82291484997289389685…89658905377877442561

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 #365,880

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