Block #480,050

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/8/2014, 1:56:38 AM · Difficulty 10.5123 · 6,315,939 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

03d5479f9e7a700ceb0648de7f902e67b6e9b79ec3ff331b843e16c2e78eee3f

View on Chainz ↗

Height

#480,050

Difficulty

10.512320

Transactions

Size

1.01 KB

Version

Bits

0a83276c

Nonce

171,627

Timestamp

4/8/2014, 1:56:38 AM

Confirmations

6,315,939

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

395943a453454095ee2a637ff8832610185ab443b5867e4e0533cb73c575c213

Transactions (5)

Coinbase4512cf5c06243b…83ab048b7cd0ff

1 in → 1 out9.0700 XPM110 B

AeKNrjNj…1NEq95Ta

b63971cac97bd3…7e68d7da299e4f

1 in → 1 out9.1400 XPM158 B

ATV4M1CV…dd9zw8nH

a0bcf738fd8144…108e9b20b8d1b9

1 in → 2 out9.0900 XPM225 B

AKveYwcS…efYDYrtd AdUqKcng…UEw88cMw

e64aa1eb0f6d24…f01c05a36d9ee5

1 in → 2 out9.0900 XPM227 B

AZkarijg…Py7EXfNT ATQkaAWH…77jvMB9e

26f9f2dd62e3fc…2c5bd8a2f20033

1 in → 2 out9.0900 XPM227 B

AX2ZQsEV…Dq5e7v24 AZUKZE6o…THAUS7R9

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.

1.607 × 10⁹⁸(99-digit number)

16077884123074982140…93878799929982863359

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

1.607 × 10⁹⁸(99-digit number)

16077884123074982140…93878799929982863359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.607 × 10⁹⁸(99-digit number)

16077884123074982140…93878799929982863361

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

3.215 × 10⁹⁸(99-digit number)

32155768246149964280…87757599859965726719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.215 × 10⁹⁸(99-digit number)

32155768246149964280…87757599859965726721

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

6.431 × 10⁹⁸(99-digit number)

64311536492299928560…75515199719931453439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.431 × 10⁹⁸(99-digit number)

64311536492299928560…75515199719931453441

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

1.286 × 10⁹⁹(100-digit number)

12862307298459985712…51030399439862906879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.286 × 10⁹⁹(100-digit number)

12862307298459985712…51030399439862906881

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

2.572 × 10⁹⁹(100-digit number)

25724614596919971424…02060798879725813759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.572 × 10⁹⁹(100-digit number)

25724614596919971424…02060798879725813761

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