Block #398,579

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/10/2014, 7:53:53 PM · Difficulty 10.4253 · 6,409,448 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

81ce710ea9e855d3c652d137523c86165bf9b58a19570bdba6288c3bc4d93c72

View on Chainz ↗

Height

#398,579

Difficulty

10.425315

Transactions

Size

969 B

Version

Bits

0a6ce176

Nonce

96,327

Timestamp

2/10/2014, 7:53:53 PM

Confirmations

6,409,448

Mined by

⛏️ aR.GAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

285bb20dad8a2e91385f2d6878351f36cdcff5ece0ef9198c703dae23763f9ab

Transactions (1)

Coinbase285bb20dad8a2e…03dae23763f9ab

1 in → 24 out9.1900 XPM879 B

AQvZBsUo…hppgRZTJ AXX1wTMN…FfSE8V61 Aac9Hjdg…P4ktypc3 ATKK7iFz…wZm46KN1 AGKhfQo2…h7fBXLX6

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.

2.945 × 10⁹³(94-digit number)

29459396661385366072…94947379238728110479

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

2.945 × 10⁹³(94-digit number)

29459396661385366072…94947379238728110479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.945 × 10⁹³(94-digit number)

29459396661385366072…94947379238728110481

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

5.891 × 10⁹³(94-digit number)

58918793322770732145…89894758477456220959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.891 × 10⁹³(94-digit number)

58918793322770732145…89894758477456220961

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

1.178 × 10⁹⁴(95-digit number)

11783758664554146429…79789516954912441919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.178 × 10⁹⁴(95-digit number)

11783758664554146429…79789516954912441921

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

2.356 × 10⁹⁴(95-digit number)

23567517329108292858…59579033909824883839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.356 × 10⁹⁴(95-digit number)

23567517329108292858…59579033909824883841

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

4.713 × 10⁹⁴(95-digit number)

47135034658216585716…19158067819649767679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.713 × 10⁹⁴(95-digit number)

47135034658216585716…19158067819649767681

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 #398,579

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