Block #399,844

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/11/2014, 4:12:09 PM · Difficulty 10.4315 · 6,394,959 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7b71e12b9bf877d7118731d59c4fe07eef1a5b13e72bdf096bf52191b97803ee

View on Chainz ↗

Height

#399,844

Difficulty

10.431534

Transactions

Size

547 B

Version

Bits

0a6e78ff

Nonce

176,511

Timestamp

2/11/2014, 4:12:09 PM

Confirmations

6,394,959

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

21e96c244a86f178f98599465582b8cce7bbf5002a4f6801966ff8fdf944aff9

Transactions (2)

Coinbasedf67a53c60f38d…f7ca5b5e43a3b9

1 in → 1 out9.1962 XPM116 B

AbwWkWZt…kawDhufa

b384a501eaa5c6…69e3c4cb221e40

2 in → 1 out1.0000 XPM340 B

Ac8knWXR…uUMyn63E

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.

2.280 × 10⁹⁶(97-digit number)

22807077676445735862…24292162204306238159

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

2.280 × 10⁹⁶(97-digit number)

22807077676445735862…24292162204306238159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.280 × 10⁹⁶(97-digit number)

22807077676445735862…24292162204306238161

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

4.561 × 10⁹⁶(97-digit number)

45614155352891471725…48584324408612476319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.561 × 10⁹⁶(97-digit number)

45614155352891471725…48584324408612476321

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

9.122 × 10⁹⁶(97-digit number)

91228310705782943450…97168648817224952639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.122 × 10⁹⁶(97-digit number)

91228310705782943450…97168648817224952641

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

1.824 × 10⁹⁷(98-digit number)

18245662141156588690…94337297634449905279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.824 × 10⁹⁷(98-digit number)

18245662141156588690…94337297634449905281

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

3.649 × 10⁹⁷(98-digit number)

36491324282313177380…88674595268899810559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.649 × 10⁹⁷(98-digit number)

36491324282313177380…88674595268899810561

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