Block #472,024

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/2/2014, 11:57:43 PM · Difficulty 10.4352 · 6,352,672 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c93e3c227e30a534f6652480deb68915159718c0e84a88b2f2fc141b02be8ea3

View on Chainz ↗

Height

#472,024

Difficulty

10.435245

Transactions

Size

830 B

Version

Bits

0a6f6c3c

Nonce

152,130

Timestamp

4/2/2014, 11:57:43 PM

Confirmations

6,352,672

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

59b19f12ad7dbd44d7ab56ab08f8bccc4f580d411581d2299e5c6796b712ebdb

Transactions (2)

Coinbase8ec0fd9815441c…25d9de65705bbf

1 in → 1 out9.1800 XPM116 B

AbwWkWZt…kawDhufa

82bf18a4099cd3…b0069f81683b8e

3 in → 8 out27.5300 XPM623 B

AeKNrjNj…1NEq95Ta AeGdqZdp…fbd4rTx5 AbTkHq49…Eo1k1gXY AcBnBiUw…CYFN81QZ ALHBdz1N…v6hU6ZDR

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.

1.796 × 10⁹⁸(99-digit number)

17969501328796943819…69736314700194911999

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

1.796 × 10⁹⁸(99-digit number)

17969501328796943819…69736314700194911999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.796 × 10⁹⁸(99-digit number)

17969501328796943819…69736314700194912001

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

3.593 × 10⁹⁸(99-digit number)

35939002657593887638…39472629400389823999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.593 × 10⁹⁸(99-digit number)

35939002657593887638…39472629400389824001

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

7.187 × 10⁹⁸(99-digit number)

71878005315187775277…78945258800779647999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.187 × 10⁹⁸(99-digit number)

71878005315187775277…78945258800779648001

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

1.437 × 10⁹⁹(100-digit number)

14375601063037555055…57890517601559295999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.437 × 10⁹⁹(100-digit number)

14375601063037555055…57890517601559296001

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

2.875 × 10⁹⁹(100-digit number)

28751202126075110110…15781035203118591999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.875 × 10⁹⁹(100-digit number)

28751202126075110110…15781035203118592001

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 #472,024

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