Block #482,286

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/9/2014, 11:09:28 AM · Difficulty 10.5422 · 6,316,283 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1c2706a29cfe32440f8dd2544a210b0fc849a46f9e818305cdc917500119331b

View on Chainz ↗

Height

#482,286

Difficulty

10.542188

Transactions

Size

804 B

Version

Bits

0a8accd7

Nonce

122,672

Timestamp

4/9/2014, 11:09:28 AM

Confirmations

6,316,283

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

7f75543a6b20f9ac14ac196b815b98247e2d3a177d5f6581a870e7745a27e7b6

Transactions (3)

Coinbase1fa99e32d5030d…163929d5168d64

1 in → 1 out9.0000 XPM110 B

AeKNrjNj…1NEq95Ta

5dc832173e39b7…cee621ed852701

2 in → 2 out15.7536 XPM375 B

AQZTJksR…idXWuK9p AJs8bhpw…KMYhBkAv

f6ee40b3bab116…e5e148a7f3c7c7

1 in → 2 out7.0282 XPM227 B

AXxp24rY…yi3yUFBu AMf9s173…q25QEeRZ

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.

8.067 × 10⁹⁸(99-digit number)

80679299791475270060…78259067637150020359

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

8.067 × 10⁹⁸(99-digit number)

80679299791475270060…78259067637150020359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.067 × 10⁹⁸(99-digit number)

80679299791475270060…78259067637150020361

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

1.613 × 10⁹⁹(100-digit number)

16135859958295054012…56518135274300040719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.613 × 10⁹⁹(100-digit number)

16135859958295054012…56518135274300040721

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

3.227 × 10⁹⁹(100-digit number)

32271719916590108024…13036270548600081439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.227 × 10⁹⁹(100-digit number)

32271719916590108024…13036270548600081441

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

6.454 × 10⁹⁹(100-digit number)

64543439833180216048…26072541097200162879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.454 × 10⁹⁹(100-digit number)

64543439833180216048…26072541097200162881

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

1.290 × 10¹⁰⁰(101-digit number)

12908687966636043209…52145082194400325759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.290 × 10¹⁰⁰(101-digit number)

12908687966636043209…52145082194400325761

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