Block #92,709

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/1/2013, 9:34:33 PM · Difficulty 9.2035 · 6,699,009 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2af53c9b9a739075c0b1ba03947df583d0d2cd1de563a89593fbf3104c610b53

View on Chainz ↗

Height

#92,709

Difficulty

9.203463

Transactions

Size

199 B

Version

Bits

0934162d

Nonce

51,744

Timestamp

8/1/2013, 9:34:33 PM

Confirmations

6,699,009

Merkle Root

88e555e7b51a9452fe803a5c286f85ac3bd34a5e27f593c94ac1676ee2550429

Transactions (1)

Coinbase88e555e7b51a94…c1676ee2550429

1 in → 1 out11.7900 XPM109 B

AWuDuxGX…tLDpHWp7

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.

6.712 × 10⁹⁵(96-digit number)

67120363355448269835…70572983107859324699

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

6.712 × 10⁹⁵(96-digit number)

67120363355448269835…70572983107859324699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.712 × 10⁹⁵(96-digit number)

67120363355448269835…70572983107859324701

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

1.342 × 10⁹⁶(97-digit number)

13424072671089653967…41145966215718649399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.342 × 10⁹⁶(97-digit number)

13424072671089653967…41145966215718649401

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

2.684 × 10⁹⁶(97-digit number)

26848145342179307934…82291932431437298799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.684 × 10⁹⁶(97-digit number)

26848145342179307934…82291932431437298801

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

5.369 × 10⁹⁶(97-digit number)

53696290684358615868…64583864862874597599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.369 × 10⁹⁶(97-digit number)

53696290684358615868…64583864862874597601

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

1.073 × 10⁹⁷(98-digit number)

10739258136871723173…29167729725749195199

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