Block #440,168

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/12/2014, 6:15:05 AM · Difficulty 10.3505 · 6,354,766 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2c6bd2cfd273a3905d5dc38481154ae6da3407fbd54ddd23f7882de67b402270

View on Chainz ↗

Height

#440,168

Difficulty

10.350523

Transactions

Size

1.82 KB

Version

Bits

0a59bbe8

Nonce

471,473

Timestamp

3/12/2014, 6:15:05 AM

Confirmations

6,354,766

Mined by

⛏️ ho!AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

79633e25c299ec91c64983e4f8469ee0d503054a2e5da0d4c7d0848d4bec575f

Transactions (2)

Coinbase18f422bd865c34…5f8b17ba80633b

1 in → 22 out9.3300 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw Adbb4svj…dQWTHsq5 ASgUri65…C7NLcyBg ATp4jJhs…TbSgR8Qb

90b37f7505e404…cdaae87456f01c

6 in → 2 out15.0753 XPM964 B

Aa5mrKR8…nm7PAEty AU3m5wJG…KrpmYFti

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.

9.606 × 10⁹⁵(96-digit number)

96064237792557338689…56927128308183960319

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

9.606 × 10⁹⁵(96-digit number)

96064237792557338689…56927128308183960319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.606 × 10⁹⁵(96-digit number)

96064237792557338689…56927128308183960321

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

1.921 × 10⁹⁶(97-digit number)

19212847558511467737…13854256616367920639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.921 × 10⁹⁶(97-digit number)

19212847558511467737…13854256616367920641

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

3.842 × 10⁹⁶(97-digit number)

38425695117022935475…27708513232735841279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.842 × 10⁹⁶(97-digit number)

38425695117022935475…27708513232735841281

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

7.685 × 10⁹⁶(97-digit number)

76851390234045870951…55417026465471682559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.685 × 10⁹⁶(97-digit number)

76851390234045870951…55417026465471682561

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

1.537 × 10⁹⁷(98-digit number)

15370278046809174190…10834052930943365119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.537 × 10⁹⁷(98-digit number)

15370278046809174190…10834052930943365121

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