Block #480,104

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/8/2014, 2:42:12 AM · Difficulty 10.5132 · 6,321,675 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5309e5cde58858aa8d736b68de8bb87e806c07272412efd0121159b9f4888d80

View on Chainz ↗

Height

#480,104

Difficulty

10.513249

Transactions

Size

1.03 KB

Version

Bits

0a836451

Nonce

23,498

Timestamp

4/8/2014, 2:42:12 AM

Confirmations

6,321,675

Mined by

⛏️ hSaSCambANNg88pGRQwFs2RfTXspDobTEJppn21sTe

Merkle Root

d737d367a74dbfb17462d3d6add6775d09aed8ed27ed4f425a95111e8f667bc5

Transactions (2)

Coinbase5fa11d42b39eec…3e5c4f9278b57b

1 in → 21 out9.0295 XPM777 B

ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 AWMrD5hP…ZwsoxvZ3 ALqxX1WA…hsKjbnXn

18e985038dbea9…1fb59fa89b434f

1 in → 1 out0.3562 XPM191 B

AGXFqSyj…FxquNuxH

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.

3.446 × 10⁹³(94-digit number)

34466537584750093975…49540680239041364959

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

3.446 × 10⁹³(94-digit number)

34466537584750093975…49540680239041364959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.446 × 10⁹³(94-digit number)

34466537584750093975…49540680239041364961

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

6.893 × 10⁹³(94-digit number)

68933075169500187951…99081360478082729919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.893 × 10⁹³(94-digit number)

68933075169500187951…99081360478082729921

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

1.378 × 10⁹⁴(95-digit number)

13786615033900037590…98162720956165459839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.378 × 10⁹⁴(95-digit number)

13786615033900037590…98162720956165459841

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

2.757 × 10⁹⁴(95-digit number)

27573230067800075180…96325441912330919679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.757 × 10⁹⁴(95-digit number)

27573230067800075180…96325441912330919681

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

5.514 × 10⁹⁴(95-digit number)

55146460135600150361…92650883824661839359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.514 × 10⁹⁴(95-digit number)

55146460135600150361…92650883824661839361

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