Block #442,642

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/13/2014, 11:42:32 PM · Difficulty 10.3490 · 6,382,726 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5167571455193f9b05ae69c5e344ac297938d35001bcac62185b55100aa521d5

View on Chainz ↗

Height

#442,642

Difficulty

10.349002

Transactions

Size

535 B

Version

Bits

0a595830

Nonce

2,611

Timestamp

3/13/2014, 11:42:32 PM

Confirmations

6,382,726

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

143b7c15ffb89cf2f9423ebe859610a8c61f71feaf43937e62ca5ea88930a7a9

Transactions (2)

Coinbase26233bacabd5c2…80bbadfde41be7

1 in → 1 out9.3300 XPM116 B

AbwWkWZt…kawDhufa

f561e0e901eeab…6a608639ba52b4

1 in → 6 out9.3000 XPM327 B

AHpZVsQR…c5YYRgif AU9KdB9r…o5XC6WMy AWWYSv6U…ez7DXzi1 AWpN9SZ7…cfg39PDg AYafpBc8…z9k6vd26

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.

2.222 × 10¹⁰⁰(101-digit number)

22224449130981962593…57714144911973319039

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

2.222 × 10¹⁰⁰(101-digit number)

22224449130981962593…57714144911973319039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.222 × 10¹⁰⁰(101-digit number)

22224449130981962593…57714144911973319041

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

4.444 × 10¹⁰⁰(101-digit number)

44448898261963925187…15428289823946638079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.444 × 10¹⁰⁰(101-digit number)

44448898261963925187…15428289823946638081

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

8.889 × 10¹⁰⁰(101-digit number)

88897796523927850374…30856579647893276159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.889 × 10¹⁰⁰(101-digit number)

88897796523927850374…30856579647893276161

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

1.777 × 10¹⁰¹(102-digit number)

17779559304785570074…61713159295786552319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.777 × 10¹⁰¹(102-digit number)

17779559304785570074…61713159295786552321

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

3.555 × 10¹⁰¹(102-digit number)

35559118609571140149…23426318591573104639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.555 × 10¹⁰¹(102-digit number)

35559118609571140149…23426318591573104641

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 #442,642

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