Block #92,247

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/1/2013, 1:50:23 PM · Difficulty 9.2038 · 6,712,838 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4a90b1b12b84ff6b841f241f4d43776493f851c1af35a54a8701c9cfecf04102

View on Chainz ↗

Height

#92,247

Difficulty

9.203751

Transactions

Size

646 B

Version

Bits

09342908

Nonce

27,601

Timestamp

8/1/2013, 1:50:23 PM

Confirmations

6,712,838

Mined by

⛏️ P2SHAW3wk4PCDzSdGxjLQDPaUtFa9gGdeyfXbD

Merkle Root

70a3d3cff4a94fcda64fd7f6a1c933147dd0c16f1d6ba2f20a62fc501606eebc

Transactions (2)

Coinbase62f65725fad617…2eeb045d7e84c3

1 in → 1 out11.8000 XPM109 B

AW3wk4PC…GdeyfXbD

b3803ea240af66…c776741985603b

2 in → 4 out2.5107 XPM442 B

AMdf2JPw…URZXPvPS AYMpcVoL…q4uwzeTU ALsdzV4L…EYadbJSM AKX3LgUZ…egfCwBM7

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.

8.721 × 10¹⁰⁶(107-digit number)

87215085997016233412…83523082006374698019

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

8.721 × 10¹⁰⁶(107-digit number)

87215085997016233412…83523082006374698019

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.721 × 10¹⁰⁶(107-digit number)

87215085997016233412…83523082006374698021

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

1.744 × 10¹⁰⁷(108-digit number)

17443017199403246682…67046164012749396039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.744 × 10¹⁰⁷(108-digit number)

17443017199403246682…67046164012749396041

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

3.488 × 10¹⁰⁷(108-digit number)

34886034398806493364…34092328025498792079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.488 × 10¹⁰⁷(108-digit number)

34886034398806493364…34092328025498792081

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

6.977 × 10¹⁰⁷(108-digit number)

69772068797612986729…68184656050997584159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.977 × 10¹⁰⁷(108-digit number)

69772068797612986729…68184656050997584161

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

1.395 × 10¹⁰⁸(109-digit number)

13954413759522597345…36369312101995168319

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