Block #383,629

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/31/2014, 1:17:30 PM · Difficulty 10.4023 · 6,411,150 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c44f2acba5cad7d50fde73625c9512eeeb5cf98f80bbbe851737ff5c3b9f65f0

View on Chainz ↗

Height

#383,629

Difficulty

10.402335

Transactions

Size

1.95 KB

Version

Bits

0a66ff6e

Nonce

67,421

Timestamp

1/31/2014, 1:17:30 PM

Confirmations

6,411,150

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

1d9b0cb4ebd064dfc7d74593655315100649f38b18c005f03cbe0cdca58ac627

Transactions (5)

Coinbasef3ed31c981d530…9c02749b120aff

1 in → 1 out9.2700 XPM116 B

AbwWkWZt…kawDhufa

90d68dfc429bfc…588a5c8a965fe2

2 in → 2 out10.2815 XPM376 B

AZ1Jbu9J…x99FxdQK APaSkzEP…e9f176Qr

c11caf7e666432…c4abd0da23f30e

6 in → 2 out10.0422 XPM965 B

AMB491YH…qXN4yJep AZpixDrq…gHXgZyha

f3fae8ef7211c8…100cf1b5c2ea4d

1 in → 2 out5.0295 XPM225 B

AdEDWNFn…7DoWbJYV AXy8CJrT…rHLoyh3A

37ad91f2a8a79e…51b57f029a04f4

1 in → 2 out3.0418 XPM227 B

AU6a7fJ5…5ouhZY6d AbYUts71…PB7itDtN

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.

2.874 × 10⁹⁸(99-digit number)

28748872009847854500…08726839859279675199

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

2.874 × 10⁹⁸(99-digit number)

28748872009847854500…08726839859279675199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.874 × 10⁹⁸(99-digit number)

28748872009847854500…08726839859279675201

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

5.749 × 10⁹⁸(99-digit number)

57497744019695709000…17453679718559350399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.749 × 10⁹⁸(99-digit number)

57497744019695709000…17453679718559350401

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

1.149 × 10⁹⁹(100-digit number)

11499548803939141800…34907359437118700799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.149 × 10⁹⁹(100-digit number)

11499548803939141800…34907359437118700801

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

2.299 × 10⁹⁹(100-digit number)

22999097607878283600…69814718874237401599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.299 × 10⁹⁹(100-digit number)

22999097607878283600…69814718874237401601

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

4.599 × 10⁹⁹(100-digit number)

45998195215756567200…39629437748474803199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.599 × 10⁹⁹(100-digit number)

45998195215756567200…39629437748474803201

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