Block #162,419

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/13/2013, 7:29:05 AM · Difficulty 9.8611 · 6,647,668 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f84c5968d943d85c77fbceeafe0d076cc76ad367ee6d58a44dd61adb01093a0

View on Chainz ↗

Height

#162,419

Difficulty

9.861115

Transactions

Size

460 B

Version

Bits

09dc7210

Nonce

41,305

Timestamp

9/13/2013, 7:29:05 AM

Confirmations

6,647,668

Mined by

⛏️ P2SHAMFkKVcbthYfybM21VeAqtSFS6jCF37NqX

Merkle Root

464c91b791e21d405dec8a637589e53ef4c84637dce81415b220f42f989b7776

Transactions (2)

Coinbase1c49c66bbb4ec4…2f38ebedcdd1c4

1 in → 1 out10.2800 XPM109 B

AMFkKVcb…jCF37NqX

8ab50a5be2dc51…35dcedda48836a

1 in → 4 out10.2500 XPM261 B

AU5g73DE…hY8WccpK AZ8JeFHe…ZRjNzXz6 AShn9D3C…qrVJVyMe AcyPVp7N…dDULWcdA

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.

1.418 × 10⁹⁵(96-digit number)

14187536828686643393…45767199741222793599

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

1.418 × 10⁹⁵(96-digit number)

14187536828686643393…45767199741222793599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.418 × 10⁹⁵(96-digit number)

14187536828686643393…45767199741222793601

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

2.837 × 10⁹⁵(96-digit number)

28375073657373286787…91534399482445587199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.837 × 10⁹⁵(96-digit number)

28375073657373286787…91534399482445587201

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

5.675 × 10⁹⁵(96-digit number)

56750147314746573574…83068798964891174399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.675 × 10⁹⁵(96-digit number)

56750147314746573574…83068798964891174401

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

1.135 × 10⁹⁶(97-digit number)

11350029462949314714…66137597929782348799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.135 × 10⁹⁶(97-digit number)

11350029462949314714…66137597929782348801

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

2.270 × 10⁹⁶(97-digit number)

22700058925898629429…32275195859564697599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.270 × 10⁹⁶(97-digit number)

22700058925898629429…32275195859564697601

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 #162,419

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