Block #446,092

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/16/2014, 7:53:51 AM · Difficulty 10.3618 · 6,366,958 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f40b0e1d0701d8db6daa6042fa06d7007c186dcd3191a3d9395c02792d45e42a

View on Chainz ↗

Height

#446,092

Difficulty

10.361841

Transactions

Size

358 B

Version

Bits

0a5ca195

Nonce

384,790

Timestamp

3/16/2014, 7:53:51 AM

Confirmations

6,366,958

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

fdbfd5920a1ed59be99cca4497000c155d4597cb7e61758df417dc822d3554b1

Transactions (2)

Coinbase094d4c1caab535…798e41d3230dc9

1 in → 1 out9.3100 XPM110 B

AeKNrjNj…1NEq95Ta

72f228e4a6deef…4e027a93a59d09

1 in → 1 out9.3900 XPM158 B

AduVrPTV…jQRoCrBT

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.

2.189 × 10⁹⁵(96-digit number)

21899996022551264265…73759476003478661119

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

2.189 × 10⁹⁵(96-digit number)

21899996022551264265…73759476003478661119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.189 × 10⁹⁵(96-digit number)

21899996022551264265…73759476003478661121

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

4.379 × 10⁹⁵(96-digit number)

43799992045102528530…47518952006957322239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.379 × 10⁹⁵(96-digit number)

43799992045102528530…47518952006957322241

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

8.759 × 10⁹⁵(96-digit number)

87599984090205057061…95037904013914644479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.759 × 10⁹⁵(96-digit number)

87599984090205057061…95037904013914644481

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

1.751 × 10⁹⁶(97-digit number)

17519996818041011412…90075808027829288959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.751 × 10⁹⁶(97-digit number)

17519996818041011412…90075808027829288961

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

3.503 × 10⁹⁶(97-digit number)

35039993636082022824…80151616055658577919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.503 × 10⁹⁶(97-digit number)

35039993636082022824…80151616055658577921

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 #446,092

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