Block #483,612

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2014, 3:45:59 AM · Difficulty 10.5660 · 6,311,150 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

901265a66767a8a23bc45660b5d26bc15f6b4d9c8a43b26a2c89aa6b06fae604

View on Chainz ↗

Height

#483,612

Difficulty

10.565984

Transactions

Size

1.46 KB

Version

Bits

0a90e454

Nonce

821,342,193

Timestamp

4/10/2014, 3:45:59 AM

Confirmations

6,311,150

Mined by

⛏️ P2SHAcdbw4eQYoTnxz2D1jx9BNuDCxw2Y6kjNn

Merkle Root

95ee79e6784885bcd6c842af72bf0787cd24a0f9e8c37fda2263be236f37a739

Transactions (4)

Coinbase06a4bae3d087cd…51405144429880

1 in → 1 out8.9700 XPM109 B

Acdbw4eQ…w2Y6kjNn

b5e326fe6789f6…a4af0ac350c763

4 in → 10 out28.9475 XPM840 B

ARxZwSxP…48ZKixP1 AKRt6uwL…VYA8uNG3 AeotpmGC…wXWBzvh3 ANt8CsTm…XxNi34u4 AP6XU4Ao…mq8mf6N9

adce0d9676b285…e1cd2bb673020f

1 in → 2 out4.9574 XPM225 B

AWyaREH6…ytZFQuM9 APfH1y47…dxXKNM9L

03ae85964cf24c…708dd74f73aed7

1 in → 2 out4.9370 XPM227 B

AQfdEonB…ksrmSB1m AZPJnDt2…gjGjb9fD

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.

5.145 × 10⁹³(94-digit number)

51450330360097832193…83884282705191514349

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

5.145 × 10⁹³(94-digit number)

51450330360097832193…83884282705191514349

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.145 × 10⁹³(94-digit number)

51450330360097832193…83884282705191514351

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

1.029 × 10⁹⁴(95-digit number)

10290066072019566438…67768565410383028699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.029 × 10⁹⁴(95-digit number)

10290066072019566438…67768565410383028701

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

2.058 × 10⁹⁴(95-digit number)

20580132144039132877…35537130820766057399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.058 × 10⁹⁴(95-digit number)

20580132144039132877…35537130820766057401

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

4.116 × 10⁹⁴(95-digit number)

41160264288078265755…71074261641532114799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.116 × 10⁹⁴(95-digit number)

41160264288078265755…71074261641532114801

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

8.232 × 10⁹⁴(95-digit number)

82320528576156531510…42148523283064229599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.232 × 10⁹⁴(95-digit number)

82320528576156531510…42148523283064229601

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