Block #274,385

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 6:43:38 AM · Difficulty 9.9573 · 6,531,929 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d774e35c7378f238e501be2208d34289b0853931efd6b00261880234d505a29

View on Chainz ↗

Height

#274,385

Difficulty

9.957256

Transactions

Size

1.89 KB

Version

Bits

09f50eb8

Nonce

10,092

Timestamp

11/26/2013, 6:43:38 AM

Confirmations

6,531,929

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

3bc8f8eef1c467392dd9a1aa54b782a5386e9d157b413c9b764405be3c57d44b

Transactions (2)

Coinbase62d803dcc7eeeb…c51b7f61a2c079

1 in → 2 out10.0900 XPM140 B

AKcbk49N…GJbKa7j1 Abiw8n3q…ZnZfgvQW

0df247182f6bec…609bd6528977ac

11 in → 2 out104.0100 XPM1.66 KB

AaDsEEVX…PoHUXss5 AKp37yGw…VWcTp4Me

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.

1.036 × 10¹⁰⁵(106-digit number)

10364332817027137806…51743529159731161599

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

1.036 × 10¹⁰⁵(106-digit number)

10364332817027137806…51743529159731161599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.036 × 10¹⁰⁵(106-digit number)

10364332817027137806…51743529159731161601

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

2.072 × 10¹⁰⁵(106-digit number)

20728665634054275613…03487058319462323199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.072 × 10¹⁰⁵(106-digit number)

20728665634054275613…03487058319462323201

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

4.145 × 10¹⁰⁵(106-digit number)

41457331268108551226…06974116638924646399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.145 × 10¹⁰⁵(106-digit number)

41457331268108551226…06974116638924646401

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

8.291 × 10¹⁰⁵(106-digit number)

82914662536217102452…13948233277849292799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.291 × 10¹⁰⁵(106-digit number)

82914662536217102452…13948233277849292801

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

1.658 × 10¹⁰⁶(107-digit number)

16582932507243420490…27896466555698585599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.658 × 10¹⁰⁶(107-digit number)

16582932507243420490…27896466555698585601

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 #274,385

Cookie Preferences