Block #792,942

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/2/2014, 12:10:17 AM · Difficulty 10.9739 · 6,033,818 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

df3552b1880344245a7f5e6d56e2addb81daebac860d246dcf9e29c69e0a1705

View on Chainz ↗

Height

#792,942

Difficulty

10.973946

Transactions

Size

432 B

Version

Bits

0af95482

Nonce

1,882,147,993

Timestamp

11/2/2014, 12:10:17 AM

Confirmations

6,033,818

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

60af3f865b1b373624351d85ddb0ce1e1b6a1ab4fb1b7bc42ea4964397132f1c

Transactions (2)

Coinbase731e4198799e89…1201123817cb28

1 in → 1 out8.3000 XPM116 B

ANSXnLY2…Sd25TjkD

dc3677676490bc…baa622c0bc8acd

1 in → 2 out3.7517 XPM226 B

Ad9ygyTf…jNFpKfiv APArSasz…sEoPxKri

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.

2.224 × 10⁹⁴(95-digit number)

22247919420335269043…30431196951965801719

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

2.224 × 10⁹⁴(95-digit number)

22247919420335269043…30431196951965801719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.224 × 10⁹⁴(95-digit number)

22247919420335269043…30431196951965801721

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

4.449 × 10⁹⁴(95-digit number)

44495838840670538087…60862393903931603439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.449 × 10⁹⁴(95-digit number)

44495838840670538087…60862393903931603441

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

8.899 × 10⁹⁴(95-digit number)

88991677681341076175…21724787807863206879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.899 × 10⁹⁴(95-digit number)

88991677681341076175…21724787807863206881

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

1.779 × 10⁹⁵(96-digit number)

17798335536268215235…43449575615726413759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.779 × 10⁹⁵(96-digit number)

17798335536268215235…43449575615726413761

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

3.559 × 10⁹⁵(96-digit number)

35596671072536430470…86899151231452827519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.559 × 10⁹⁵(96-digit number)

35596671072536430470…86899151231452827521

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 #792,942

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