Block #411,544

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/19/2014, 8:21:43 PM · Difficulty 10.4286 · 6,406,498 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a9bb9ca8d317758ada8ca7523c5fcabe87763d767c4bc97849aec7463ad811ab

View on Chainz ↗

Height

#411,544

Difficulty

10.428643

Transactions

Size

881 B

Version

Bits

0a6dbb89

Nonce

231,962

Timestamp

2/19/2014, 8:21:43 PM

Confirmations

6,406,498

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

39d571d763eb24cc0f72664d851ba13b2adab8d74588c6aa1ff7ae28e6851849

Transactions (4)

Coinbase1137ecbc4e236d…6e044798a6fd42

1 in → 1 out9.2100 XPM110 B

AeKNrjNj…1NEq95Ta

1e3187acd88544…407aea9b4a5f2a

1 in → 2 out7.1209 XPM226 B

AafXBxi8…MTbj7rvU AXEDcXoK…TFAt4d8H

0e357bff1d54ab…25b215b2706ce4

1 in → 2 out4.1098 XPM226 B

AJw6sDxr…DyXgkbgC AbRv1fC8…bDL4aVbA

412ec0280f56ad…0e8b45d54a2397

1 in → 2 out3.5462 XPM226 B

AUAfYcmQ…B3DywuZK AXGG94CH…hTtfejB8

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.

1.889 × 10¹⁰²(103-digit number)

18899759784423799816…42330883834488299519

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

1.889 × 10¹⁰²(103-digit number)

18899759784423799816…42330883834488299519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.889 × 10¹⁰²(103-digit number)

18899759784423799816…42330883834488299521

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

3.779 × 10¹⁰²(103-digit number)

37799519568847599633…84661767668976599039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.779 × 10¹⁰²(103-digit number)

37799519568847599633…84661767668976599041

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

7.559 × 10¹⁰²(103-digit number)

75599039137695199266…69323535337953198079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.559 × 10¹⁰²(103-digit number)

75599039137695199266…69323535337953198081

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

1.511 × 10¹⁰³(104-digit number)

15119807827539039853…38647070675906396159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.511 × 10¹⁰³(104-digit number)

15119807827539039853…38647070675906396161

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

3.023 × 10¹⁰³(104-digit number)

30239615655078079706…77294141351812792319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.023 × 10¹⁰³(104-digit number)

30239615655078079706…77294141351812792321

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 #411,544

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