Block #459,129

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/25/2014, 2:31:19 AM · Difficulty 10.4179 · 6,349,271 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4956c7dc8d6e8d18269a613fad4e3be1deb868d8fd65a6c9ef573fe72d397eef

View on Chainz ↗

Height

#459,129

Difficulty

10.417851

Transactions

Size

1.46 KB

Version

Bits

0a6af848

Nonce

5,387

Timestamp

3/25/2014, 2:31:19 AM

Confirmations

6,349,271

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a9885ff1d295fe90852b58f83e9b3e95d0fc1fe899466921a5d2469f4e943440

Transactions (2)

Coinbase4faa8b42b8311d…4fbc515d0bdee0

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

c4ce089294d3c2…8b1292421b488f

7 in → 10 out28.3657 XPM1.25 KB

AGTaBWB9…EMpeDDaJ AeKNrjNj…1NEq95Ta AKJx7ewq…cdjZ12Jp ATk4yXJY…yVVTNX8F AbY6jpKm…xfyDrP1G

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.

1.464 × 10⁹⁸(99-digit number)

14643965495428199666…30020140459069107539

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

1.464 × 10⁹⁸(99-digit number)

14643965495428199666…30020140459069107539

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.464 × 10⁹⁸(99-digit number)

14643965495428199666…30020140459069107541

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

2.928 × 10⁹⁸(99-digit number)

29287930990856399332…60040280918138215079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.928 × 10⁹⁸(99-digit number)

29287930990856399332…60040280918138215081

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

5.857 × 10⁹⁸(99-digit number)

58575861981712798665…20080561836276430159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.857 × 10⁹⁸(99-digit number)

58575861981712798665…20080561836276430161

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

1.171 × 10⁹⁹(100-digit number)

11715172396342559733…40161123672552860319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.171 × 10⁹⁹(100-digit number)

11715172396342559733…40161123672552860321

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

2.343 × 10⁹⁹(100-digit number)

23430344792685119466…80322247345105720639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.343 × 10⁹⁹(100-digit number)

23430344792685119466…80322247345105720641

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 #459,129

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