Block #436,495

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/9/2014, 3:17:45 PM · Difficulty 10.3610 · 6,370,409 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1b6530dad18f79ea1346649b1c775d70d48456670be7172023798f0ac0fb7474

View on Chainz ↗

Height

#436,495

Difficulty

10.360962

Transactions

Size

1.38 KB

Version

Bits

0a5c6804

Nonce

274,506

Timestamp

3/9/2014, 3:17:45 PM

Confirmations

6,370,409

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

5af7c834ef8d572973beb16fd54c09d5c7aa6f486a5de2674cf10e898d482fcc

Transactions (2)

Coinbase1ea649d75d131a…5bdacd4735dd9d

1 in → 23 out9.3000 XPM845 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ

7060a0cded6ed5…ca41e9bd5bcb38

2 in → 6 out15.8529 XPM476 B

ASLWpBFw…bjGM3fWh AbRso1mW…qkEyGERy AKenziQA…jfhjbJcR AKbpoask…dtBVWNrZ AMTJFbxj…5CD9oHk6

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.

4.940 × 10⁹⁶(97-digit number)

49408913733029769859…06472468607563452399

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

4.940 × 10⁹⁶(97-digit number)

49408913733029769859…06472468607563452399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.940 × 10⁹⁶(97-digit number)

49408913733029769859…06472468607563452401

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

9.881 × 10⁹⁶(97-digit number)

98817827466059539719…12944937215126904799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.881 × 10⁹⁶(97-digit number)

98817827466059539719…12944937215126904801

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

1.976 × 10⁹⁷(98-digit number)

19763565493211907943…25889874430253809599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.976 × 10⁹⁷(98-digit number)

19763565493211907943…25889874430253809601

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

3.952 × 10⁹⁷(98-digit number)

39527130986423815887…51779748860507619199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.952 × 10⁹⁷(98-digit number)

39527130986423815887…51779748860507619201

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

7.905 × 10⁹⁷(98-digit number)

79054261972847631775…03559497721015238399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.905 × 10⁹⁷(98-digit number)

79054261972847631775…03559497721015238401

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 #436,495

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