Block #92,265

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/1/2013, 2:14:47 PM · Difficulty 9.2027 · 6,712,822 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ffc712312d1d5bf4c53c2c7664e5326e786590ef57f291b01953e98a4dbfea75

View on Chainz ↗

Height

#92,265

Difficulty

9.202672

Transactions

Size

802 B

Version

Bits

0933e24c

Nonce

673

Timestamp

8/1/2013, 2:14:47 PM

Confirmations

6,712,822

Mined by

⛏️ P2SHAJP3RJtbkSMuRektreitYAzY723kfvuZfc

Merkle Root

fec0a5cc7c776117225ffd52ee2a5318d0557b84c7a72c116fbde5a83376a6f4

Transactions (3)

Coinbase3685d966063ffd…3eae751c9a44cb

1 in → 1 out11.8100 XPM110 B

AJP3RJtb…3kfvuZfc

2590cea6f05531…949fae316a7d1f

2 in → 2 out2.4517 XPM376 B

AP2KFX7L…j2fsRQmW AdnJA43N…SRdVK7xk

fc5f7ea7f4d5e7…5ad4fa0340640e

1 in → 2 out1.0764 XPM227 B

AMdf2JPw…URZXPvPS AKemRiqj…HBJnqwNX

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.

1.012 × 10⁹²(93-digit number)

10123754744568119625…04458750352998826519

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

1.012 × 10⁹²(93-digit number)

10123754744568119625…04458750352998826519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.012 × 10⁹²(93-digit number)

10123754744568119625…04458750352998826521

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

2.024 × 10⁹²(93-digit number)

20247509489136239251…08917500705997653039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.024 × 10⁹²(93-digit number)

20247509489136239251…08917500705997653041

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

4.049 × 10⁹²(93-digit number)

40495018978272478503…17835001411995306079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.049 × 10⁹²(93-digit number)

40495018978272478503…17835001411995306081

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

8.099 × 10⁹²(93-digit number)

80990037956544957007…35670002823990612159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.099 × 10⁹²(93-digit number)

80990037956544957007…35670002823990612161

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

1.619 × 10⁹³(94-digit number)

16198007591308991401…71340005647981224319

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