Block #448,134

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/17/2014, 5:11:51 PM · Difficulty 10.3683 · 6,368,212 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

936dd0d96597c1c2c1cc82b70f5e495dec2fa3fd64f1585a44e12a791980f5a6

View on Chainz ↗

Height

#448,134

Difficulty

10.368331

Transactions

Size

2.85 KB

Version

Bits

0a5e4af2

Nonce

26,882

Timestamp

3/17/2014, 5:11:51 PM

Confirmations

6,368,212

Mined by

⛏️ uAHQyfiZn7AWhbhzXeEptuwLriCsQbeqE98

Merkle Root

6fa5d3325f6c8793c3974279b6432594d3671fdcf0403882bfcd9f9d7c725ae2

Transactions (2)

Coinbaseda70f3fc43a1d0…4a9cccd8123e9f

1 in → 6 out9.3200 XPM267 B

AHQyfiZn…sQbeqE98 AN9emqpK…WEnrfX7s AWCjgrw2…MnFAU7HX ANKzHTAZ…nyUjaxVT AXDyRw5b…CSGugJcJ

7a2e438f52616d…303c5498f3995d

9 in → 36 out83.9000 XPM2.50 KB

AKETzsmH…Z9z4oYx7 ARapidPq…BD8pNF5M Af1Eejkx…cKmYn3YE APQCLq5D…cpNbYpoy AUkdqaxr…4jcbMUQ7

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.

8.182 × 10⁹⁷(98-digit number)

81829564329741908325…30542207503831789439

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

8.182 × 10⁹⁷(98-digit number)

81829564329741908325…30542207503831789439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.182 × 10⁹⁷(98-digit number)

81829564329741908325…30542207503831789441

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

1.636 × 10⁹⁸(99-digit number)

16365912865948381665…61084415007663578879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.636 × 10⁹⁸(99-digit number)

16365912865948381665…61084415007663578881

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

3.273 × 10⁹⁸(99-digit number)

32731825731896763330…22168830015327157759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.273 × 10⁹⁸(99-digit number)

32731825731896763330…22168830015327157761

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

6.546 × 10⁹⁸(99-digit number)

65463651463793526660…44337660030654315519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.546 × 10⁹⁸(99-digit number)

65463651463793526660…44337660030654315521

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

1.309 × 10⁹⁹(100-digit number)

13092730292758705332…88675320061308631039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.309 × 10⁹⁹(100-digit number)

13092730292758705332…88675320061308631041

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 #448,134

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