Block #1,532,530

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/8/2016, 11:03:05 PM · Difficulty 10.6131 · 5,299,509 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d8565714c51d1655469d75cfd22f29d353df8757f651f5b79f8011dbe24f04c5

View on Chainz ↗

Height

#1,532,530

Difficulty

10.613060

Transactions

Size

16.80 KB

Version

Bits

0a9cf186

Nonce

447,120,722

Timestamp

4/8/2016, 11:03:05 PM

Confirmations

5,299,509

Mined by

⛏️ P2SHAS6Sb3LtbzKdffQYfkf34G6wA6gndGM2X7

Merkle Root

8df16ead00d33ea6f9476fa3ae0651b04a2e08fcfbc3bfb405767f85c9563c67

Transactions (3)

Coinbase84f431030fe193…9147715b0b7d87

1 in → 1 out9.0400 XPM109 B

AS6Sb3Lt…gndGM2X7

2f3786e310bd1e…dcba6a97494e9e

142 in → 2 out1261.1600 XPM15.89 KB

AQqDWCVj…qQiyxA4h AVAvXJDG…boW6hx49

a82a00999a9ae2…14268a3e68f29f

1 in → 17 out139.0808 XPM735 B

AYU6QUUw…eF2J5WU5 AXDorCDc…bfaGoaGv AGezuDgF…Rc1c725a ATq9ZmaE…yXTe5o6J AN9TY3x5…eX14vkom

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.

2.434 × 10⁹⁴(95-digit number)

24347912632659702917…07402346639484230159

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

2.434 × 10⁹⁴(95-digit number)

24347912632659702917…07402346639484230159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.434 × 10⁹⁴(95-digit number)

24347912632659702917…07402346639484230161

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

4.869 × 10⁹⁴(95-digit number)

48695825265319405835…14804693278968460319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.869 × 10⁹⁴(95-digit number)

48695825265319405835…14804693278968460321

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

9.739 × 10⁹⁴(95-digit number)

97391650530638811671…29609386557936920639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.739 × 10⁹⁴(95-digit number)

97391650530638811671…29609386557936920641

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

1.947 × 10⁹⁵(96-digit number)

19478330106127762334…59218773115873841279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.947 × 10⁹⁵(96-digit number)

19478330106127762334…59218773115873841281

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

3.895 × 10⁹⁵(96-digit number)

38956660212255524668…18437546231747682559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.895 × 10⁹⁵(96-digit number)

38956660212255524668…18437546231747682561

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 #1,532,530

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