Block #190,197

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/2/2013, 8:10:37 AM · Difficulty 9.8737 · 6,619,296 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1913ded6c956d0145b1c7c1586ebd61976886b71f57b642aedb0e7c23a6aa123

View on Chainz ↗

Height

#190,197

Difficulty

9.873658

Transactions

Size

198 B

Version

Bits

09dfa809

Nonce

16,912

Timestamp

10/2/2013, 8:10:37 AM

Confirmations

6,619,296

Mined by

⛏️ P2SHAL2EWWZmctFoTxS7QgAsvUyr8tCwsD5iKb

Merkle Root

78efcbf1b1306bd5e5cad86d96939f11b0dcc217a9593843e24d944d653a590e

Transactions (1)

Coinbase78efcbf1b1306b…4d944d653a590e

1 in → 1 out10.2400 XPM109 B

AL2EWWZm…CwsD5iKb

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.

1.653 × 10⁹¹(92-digit number)

16538840292408998608…81294269604221337599

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

1.653 × 10⁹¹(92-digit number)

16538840292408998608…81294269604221337599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.653 × 10⁹¹(92-digit number)

16538840292408998608…81294269604221337601

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

3.307 × 10⁹¹(92-digit number)

33077680584817997217…62588539208442675199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.307 × 10⁹¹(92-digit number)

33077680584817997217…62588539208442675201

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

6.615 × 10⁹¹(92-digit number)

66155361169635994434…25177078416885350399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.615 × 10⁹¹(92-digit number)

66155361169635994434…25177078416885350401

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

1.323 × 10⁹²(93-digit number)

13231072233927198886…50354156833770700799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.323 × 10⁹²(93-digit number)

13231072233927198886…50354156833770700801

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

2.646 × 10⁹²(93-digit number)

26462144467854397773…00708313667541401599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #190,197

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