Block #449,087

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/18/2014, 9:16:21 AM · Difficulty 10.3671 · 6,346,576 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

92f3fd317b28457004bc9a77ebd962dc703d13941bf8d15470af1f1ea7cf0e55

View on Chainz ↗

Height

#449,087

Difficulty

10.367052

Transactions

Size

2.79 KB

Version

Bits

0a5df726

Nonce

87,769

Timestamp

3/18/2014, 9:16:21 AM

Confirmations

6,346,576

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

f04fb98a915813ebded525188129371616a05b3442a51d117e7e7671c74e4b94

Transactions (5)

Coinbasecb095312f30ebd…fe5e352cdfdc5c

1 in → 1 out9.3400 XPM110 B

AeKNrjNj…1NEq95Ta

48af4c8e3cfe55…0375c15ce95b07

6 in → 15 out48.4126 XPM1.21 KB

ARi5oPMC…yhqk7g4j Ae5BfFib…nW1Bzjon AHy24nCY…4KpVC1Hz AVrD6maY…W77cdqzz ASTcaxJ4…gURy1LJz

d495009d7b3c8f…f531aa41669f4d

6 in → 2 out18.5714 XPM964 B

ARA9SXsL…wjBKJCo1 AJwnjXVM…LRbMjpsv

be4c2d67135158…0eb19ce13f8712

1 in → 2 out4.6747 XPM225 B

AaDJiPLg…B8Q24jgb AWUDkJZw…jxtAqAH2

173b2181536d32…0fd62871b6fa99

1 in → 2 out2.4912 XPM226 B

ASMitK1F…edxUytRs ALBedt47…FP41nMsa

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.

7.326 × 10¹⁰¹(102-digit number)

73268369882820202272…61204305562292961279

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

7.326 × 10¹⁰¹(102-digit number)

73268369882820202272…61204305562292961279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.326 × 10¹⁰¹(102-digit number)

73268369882820202272…61204305562292961281

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

1.465 × 10¹⁰²(103-digit number)

14653673976564040454…22408611124585922559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.465 × 10¹⁰²(103-digit number)

14653673976564040454…22408611124585922561

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

2.930 × 10¹⁰²(103-digit number)

29307347953128080908…44817222249171845119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.930 × 10¹⁰²(103-digit number)

29307347953128080908…44817222249171845121

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

5.861 × 10¹⁰²(103-digit number)

58614695906256161817…89634444498343690239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.861 × 10¹⁰²(103-digit number)

58614695906256161817…89634444498343690241

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

1.172 × 10¹⁰³(104-digit number)

11722939181251232363…79268888996687380479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.172 × 10¹⁰³(104-digit number)

11722939181251232363…79268888996687380481

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