Block #239,444

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/2/2013, 2:40:20 AM · Difficulty 9.9543 · 6,591,899 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f34e38c2226e65348dec442faa0922356d420c813f7d726107b07fe5dfe3e5a1

View on Chainz ↗

Height

#239,444

Difficulty

9.954346

Transactions

Size

1.74 KB

Version

Bits

09f44ffd

Nonce

125,256

Timestamp

11/2/2013, 2:40:20 AM

Confirmations

6,591,899

Mined by

⛏️ TRtefAP72ZF1f4Tt3L7vBSP2XmkGsa8K2ngR7CZ

Merkle Root

5904ca45e63b3582cf092330fb95159e6b7fa290fccb050b0f46ae90eb65fb62

Transactions (1)

Coinbase5904ca45e63b35…46ae90eb65fb62

1 in → 48 out10.0600 XPM1.65 KB

AP72ZF1f…K2ngR7CZ AFqKfjez…qX9Ace3g AQtzUSwq…htAuF3yC Ac5sZcdP…kzV4eckG AcEnwywz…vZtt2xTs

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.

4.617 × 10⁹⁴(95-digit number)

46179295765675713049…96314949051957878399

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

4.617 × 10⁹⁴(95-digit number)

46179295765675713049…96314949051957878399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.617 × 10⁹⁴(95-digit number)

46179295765675713049…96314949051957878401

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

9.235 × 10⁹⁴(95-digit number)

92358591531351426098…92629898103915756799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.235 × 10⁹⁴(95-digit number)

92358591531351426098…92629898103915756801

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

1.847 × 10⁹⁵(96-digit number)

18471718306270285219…85259796207831513599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.847 × 10⁹⁵(96-digit number)

18471718306270285219…85259796207831513601

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

3.694 × 10⁹⁵(96-digit number)

36943436612540570439…70519592415663027199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.694 × 10⁹⁵(96-digit number)

36943436612540570439…70519592415663027201

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

7.388 × 10⁹⁵(96-digit number)

73886873225081140878…41039184831326054399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.388 × 10⁹⁵(96-digit number)

73886873225081140878…41039184831326054401

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 #239,444

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