Block #224,375

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/23/2013, 5:42:46 PM · Difficulty 9.9370 · 6,583,820 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c2f95ae354d18e5f2b049da83d50a87a9bbf2131c1efd8e70dc59c42906ee3e5

View on Chainz ↗

Height

#224,375

Difficulty

9.937005

Transactions

Size

651 B

Version

Bits

09efdf97

Nonce

105,589

Timestamp

10/23/2013, 5:42:46 PM

Confirmations

6,583,820

Mined by

⛏️ P2SHASUFTk3khNQApzdyBqzs5zyZu96G1byU7n

Merkle Root

ad6f43e0cb471105ff35dd03625a95f26ccc3c0cc5842386b44821737c40c072

Transactions (3)

Coinbased1def9541e1352…93d86e6a1ccb31

1 in → 1 out10.1300 XPM109 B

ASUFTk3k…6G1byU7n

2fb613529bb671…789fe4e4ec556f

1 in → 2 out10.1000 XPM225 B

AQtKDuiB…krXZkAXJ AGAf8Z9Q…ggDWo52w

d8303748e6a29e…648d682c9cd995

1 in → 2 out3.9308 XPM227 B

AW9KKM9q…MdyZNPmz APSAumdD…KmgnVafy

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.

1.008 × 10⁹⁴(95-digit number)

10087518114182602403…93346831917817963809

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

1.008 × 10⁹⁴(95-digit number)

10087518114182602403…93346831917817963809

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.008 × 10⁹⁴(95-digit number)

10087518114182602403…93346831917817963811

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

2.017 × 10⁹⁴(95-digit number)

20175036228365204806…86693663835635927619

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.017 × 10⁹⁴(95-digit number)

20175036228365204806…86693663835635927621

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

4.035 × 10⁹⁴(95-digit number)

40350072456730409612…73387327671271855239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.035 × 10⁹⁴(95-digit number)

40350072456730409612…73387327671271855241

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

8.070 × 10⁹⁴(95-digit number)

80700144913460819225…46774655342543710479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.070 × 10⁹⁴(95-digit number)

80700144913460819225…46774655342543710481

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

1.614 × 10⁹⁵(96-digit number)

16140028982692163845…93549310685087420959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #224,375

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