Block #467,147

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/30/2014, 2:17:26 PM · Difficulty 10.4347 · 6,347,729 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

491ac9020fecddcd8e7e43127fdcf0911ca3555ae269a567e1b5b86a8c77f9be

View on Chainz ↗

Height

#467,147

Difficulty

10.434667

Transactions

Size

429 B

Version

Bits

0a6f4656

Nonce

46,778

Timestamp

3/30/2014, 2:17:26 PM

Confirmations

6,347,729

Mined by

⛏️ P2SHAbV6LTn7aK9d8vDRMRQsLAwhPn2XuWYsoR

Merkle Root

a9f90ac4f5e437032153f866a0e811728df5a5fd0f2c172ed0125ca1c1b5af6c

Transactions (2)

Coinbase96c9cc2ebb7a0e…5f8c5cf5ac3740

1 in → 1 out9.1800 XPM110 B

AbV6LTn7…2XuWYsoR

1c4862a93cb87a…cc223f23fcac92

1 in → 2 out280.0930 XPM227 B

AMd27bA2…JbJ4myjf ATxd7QZe…ANRzaeah

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.

2.497 × 10⁹⁸(99-digit number)

24977661487870194344…04314239366650668799

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

2.497 × 10⁹⁸(99-digit number)

24977661487870194344…04314239366650668799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.497 × 10⁹⁸(99-digit number)

24977661487870194344…04314239366650668801

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

4.995 × 10⁹⁸(99-digit number)

49955322975740388689…08628478733301337599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.995 × 10⁹⁸(99-digit number)

49955322975740388689…08628478733301337601

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

9.991 × 10⁹⁸(99-digit number)

99910645951480777378…17256957466602675199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.991 × 10⁹⁸(99-digit number)

99910645951480777378…17256957466602675201

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

1.998 × 10⁹⁹(100-digit number)

19982129190296155475…34513914933205350399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.998 × 10⁹⁹(100-digit number)

19982129190296155475…34513914933205350401

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

3.996 × 10⁹⁹(100-digit number)

39964258380592310951…69027829866410700799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.996 × 10⁹⁹(100-digit number)

39964258380592310951…69027829866410700801

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 #467,147

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