Block #441,018

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/12/2014, 8:07:49 PM · Difficulty 10.3527 · 6,383,757 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

66b73ba451ac5419f2b732a38b3d68d72b76410acdfa605cd5f06c648f67d8e6

View on Chainz ↗

Height

#441,018

Difficulty

10.352733

Transactions

Size

858 B

Version

Bits

0a5a4cbe

Nonce

68,572

Timestamp

3/12/2014, 8:07:49 PM

Confirmations

6,383,757

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

9d3bf42e1ba95d0d4901f4e49911d4f1f32e0a1d4492722dad1812fcb2330361

Transactions (2)

Coinbase454254aa818266…d5460198fa8ba0

1 in → 1 out9.3300 XPM110 B

AeKNrjNj…1NEq95Ta

f4b5d4fccfb98d…3a696d094b7f76

3 in → 8 out24.4213 XPM657 B

ATRzXtWP…seWCGByA Abz9CAqQ…etH6XVc6 Abus1kPT…JZUv7sP1 ALy7Ra4p…8KLmryJG AJtMDaUx…bUaiUT9g

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.

3.075 × 10⁹⁶(97-digit number)

30750250311587945979…07804914901166783999

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

3.075 × 10⁹⁶(97-digit number)

30750250311587945979…07804914901166783999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.075 × 10⁹⁶(97-digit number)

30750250311587945979…07804914901166784001

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

6.150 × 10⁹⁶(97-digit number)

61500500623175891958…15609829802333567999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.150 × 10⁹⁶(97-digit number)

61500500623175891958…15609829802333568001

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

1.230 × 10⁹⁷(98-digit number)

12300100124635178391…31219659604667135999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.230 × 10⁹⁷(98-digit number)

12300100124635178391…31219659604667136001

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

2.460 × 10⁹⁷(98-digit number)

24600200249270356783…62439319209334271999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.460 × 10⁹⁷(98-digit number)

24600200249270356783…62439319209334272001

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

4.920 × 10⁹⁷(98-digit number)

49200400498540713567…24878638418668543999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.920 × 10⁹⁷(98-digit number)

49200400498540713567…24878638418668544001

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 #441,018

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