Block #92,338

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/1/2013, 3:14:12 PM · Difficulty 9.2049 · 6,706,691 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5d91702929d80ae92daae264a0f2a3c50d825bc5ac170ce33254efbf03f2c984

View on Chainz ↗

Height

#92,338

Difficulty

9.204891

Transactions

Size

208 B

Version

Bits

093473c4

Nonce

298,785

Timestamp

8/1/2013, 3:14:12 PM

Confirmations

6,706,691

Mined by

⛏️ P2SHAJwT4t7mqNZ7nwyuBKJTxL3n2nrXZrFS9k

Merkle Root

78e6ca11fd41f4f5beb5648071ec744aadac0725595e3e6921164aaa0ad985f5

Transactions (1)

Coinbase78e6ca11fd41f4…164aaa0ad985f5

1 in → 1 out11.7900 XPM109 B

AJwT4t7m…rXZrFS9k

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.

3.302 × 10¹¹⁶(117-digit number)

33025550909423052271…07891734123723333179

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

3.302 × 10¹¹⁶(117-digit number)

33025550909423052271…07891734123723333179

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.302 × 10¹¹⁶(117-digit number)

33025550909423052271…07891734123723333181

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

6.605 × 10¹¹⁶(117-digit number)

66051101818846104543…15783468247446666359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.605 × 10¹¹⁶(117-digit number)

66051101818846104543…15783468247446666361

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

1.321 × 10¹¹⁷(118-digit number)

13210220363769220908…31566936494893332719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.321 × 10¹¹⁷(118-digit number)

13210220363769220908…31566936494893332721

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

2.642 × 10¹¹⁷(118-digit number)

26420440727538441817…63133872989786665439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.642 × 10¹¹⁷(118-digit number)

26420440727538441817…63133872989786665441

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

5.284 × 10¹¹⁷(118-digit number)

52840881455076883634…26267745979573330879

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