Block #265,229

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/19/2013, 9:15:04 AM · Difficulty 9.9630 · 6,578,816 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ff74f9bf71fde56e95515b36712f5378f25c90b931cabcfc99084dab15961b43

View on Chainz ↗

Height

#265,229

Difficulty

9.963047

Transactions

Size

648 B

Version

Bits

09f68a40

Nonce

42,547

Timestamp

11/19/2013, 9:15:04 AM

Confirmations

6,578,816

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

6e8a3a27250d04d2e3265830f13d4120985a913eb4a04705724424b1916bc6e5

Transactions (3)

Coinbase84478ff2c45c10…b2e589905a8e38

1 in → 2 out10.0800 XPM140 B

AKcbk49N…GJbKa7j1 Abiw8n3q…ZnZfgvQW

f406b50f577745…d4bf1c83ed4a7a

1 in → 1 out10.0400 XPM193 B

AREJRekG…a8dWbE8j

376f73101760e0…722dd3b18603a8

1 in → 2 out5.9618 XPM225 B

ALwAo7ze…D795gyvk ARo88A54…p5fNN5SA

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.

1.004 × 10⁹⁵(96-digit number)

10046799552567192668…23881530062798514559

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

1.004 × 10⁹⁵(96-digit number)

10046799552567192668…23881530062798514559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.004 × 10⁹⁵(96-digit number)

10046799552567192668…23881530062798514561

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

2.009 × 10⁹⁵(96-digit number)

20093599105134385337…47763060125597029119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.009 × 10⁹⁵(96-digit number)

20093599105134385337…47763060125597029121

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

4.018 × 10⁹⁵(96-digit number)

40187198210268770674…95526120251194058239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.018 × 10⁹⁵(96-digit number)

40187198210268770674…95526120251194058241

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

8.037 × 10⁹⁵(96-digit number)

80374396420537541349…91052240502388116479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.037 × 10⁹⁵(96-digit number)

80374396420537541349…91052240502388116481

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

1.607 × 10⁹⁶(97-digit number)

16074879284107508269…82104481004776232959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.607 × 10⁹⁶(97-digit number)

16074879284107508269…82104481004776232961

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 #265,229

Cookie Preferences