Block #392,578

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/6/2014, 1:37:24 PM · Difficulty 10.4396 · 6,434,333 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

765941f455901286d09c745afdeb14647936dfdfa9ac28fb0c67f14be38334cc

View on Chainz ↗

Height

#392,578

Difficulty

10.439609

Transactions

Size

867 B

Version

Bits

0a708a3a

Nonce

54,029

Timestamp

2/6/2014, 1:37:24 PM

Confirmations

6,434,333

Mined by

⛏️ aR=AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c5f80b7c02eb8b9160f53c2041d8c045812e6c7a84ac3bb590adce96e7299d38

Transactions (1)

Coinbasec5f80b7c02eb8b…adce96e7299d38

1 in → 21 out9.1600 XPM777 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH

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.

1.218 × 10⁹⁵(96-digit number)

12186364973353774182…80329200078747426099

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

1.218 × 10⁹⁵(96-digit number)

12186364973353774182…80329200078747426099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.218 × 10⁹⁵(96-digit number)

12186364973353774182…80329200078747426101

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

2.437 × 10⁹⁵(96-digit number)

24372729946707548365…60658400157494852199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.437 × 10⁹⁵(96-digit number)

24372729946707548365…60658400157494852201

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

4.874 × 10⁹⁵(96-digit number)

48745459893415096730…21316800314989704399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.874 × 10⁹⁵(96-digit number)

48745459893415096730…21316800314989704401

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

9.749 × 10⁹⁵(96-digit number)

97490919786830193461…42633600629979408799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.749 × 10⁹⁵(96-digit number)

97490919786830193461…42633600629979408801

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

1.949 × 10⁹⁶(97-digit number)

19498183957366038692…85267201259958817599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.949 × 10⁹⁶(97-digit number)

19498183957366038692…85267201259958817601

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 #392,578

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