Block #489,664

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/13/2014, 10:28:46 AM · Difficulty 10.6673 · 6,322,980 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7726510da3fe9bcc7e2b789310e8de9ac8ecf91505fa989492d5397a94bdf65a

View on Chainz ↗

Height

#489,664

Difficulty

10.667254

Transactions

Size

1.44 KB

Version

Bits

0aaad12c

Nonce

11,256,079

Timestamp

4/13/2014, 10:28:46 AM

Confirmations

6,322,980

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

10174773a9c61917b4a66ec27ed41bfc8d14824a08a1aa9fe397f534e730092b

Transactions (4)

Coinbaseb3f09c2ac094a4…cc71b294f45abc

1 in → 1 out8.8000 XPM116 B

AbwWkWZt…kawDhufa

a33b5e9d1255e0…479091029c66f2

3 in → 2 out159.9101 XPM521 B

ATP6ihBz…va7MpWW8 AarDGqbd…7SdCPj76

d4d1533e2d7533…864bd81b444720

3 in → 2 out2.3227 XPM521 B

AQxuAjby…xt1RWP1v AUWjQP8g…KtRxkZah

9619bc2edd1d09…b7783033e1a5cd

1 in → 2 out3.2480 XPM225 B

AadZp7KU…RtQKYK9y AJ4qgR5b…Duw6x7MH

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.

3.190 × 10⁹⁷(98-digit number)

31904072640974554243…61196473078490221439

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

3.190 × 10⁹⁷(98-digit number)

31904072640974554243…61196473078490221439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.190 × 10⁹⁷(98-digit number)

31904072640974554243…61196473078490221441

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

6.380 × 10⁹⁷(98-digit number)

63808145281949108486…22392946156980442879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.380 × 10⁹⁷(98-digit number)

63808145281949108486…22392946156980442881

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

1.276 × 10⁹⁸(99-digit number)

12761629056389821697…44785892313960885759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.276 × 10⁹⁸(99-digit number)

12761629056389821697…44785892313960885761

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

2.552 × 10⁹⁸(99-digit number)

25523258112779643394…89571784627921771519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.552 × 10⁹⁸(99-digit number)

25523258112779643394…89571784627921771521

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

5.104 × 10⁹⁸(99-digit number)

51046516225559286789…79143569255843543039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.104 × 10⁹⁸(99-digit number)

51046516225559286789…79143569255843543041

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 #489,664

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