Block #90,402

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/31/2013, 2:20:30 AM · Difficulty 9.2472 · 6,705,286 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cc503be70d4fc261f9f819dd6558bd65b4dd6553a26f1802846f3f43391a843f

View on Chainz ↗

Height

#90,402

Difficulty

9.247237

Transactions

Size

206 B

Version

Bits

093f4af2

Nonce

39,732

Timestamp

7/31/2013, 2:20:30 AM

Confirmations

6,705,286

Mined by

⛏️ P2SHATzEHZ7ayQf8Js5VJS7Me8qrBi2eAGweip

Merkle Root

4adcf770af563c1c04c7673eb9dcc5d22431e0894d544053a83a69b9fb56dd72

Transactions (1)

Coinbase4adcf770af563c…3a69b9fb56dd72

1 in → 1 out11.6800 XPM109 B

ATzEHZ7a…2eAGweip

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.

3.121 × 10¹¹⁰(111-digit number)

31217973733508055400…51598579365068309659

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

3.121 × 10¹¹⁰(111-digit number)

31217973733508055400…51598579365068309659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.121 × 10¹¹⁰(111-digit number)

31217973733508055400…51598579365068309661

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

6.243 × 10¹¹⁰(111-digit number)

62435947467016110801…03197158730136619319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.243 × 10¹¹⁰(111-digit number)

62435947467016110801…03197158730136619321

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

1.248 × 10¹¹¹(112-digit number)

12487189493403222160…06394317460273238639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.248 × 10¹¹¹(112-digit number)

12487189493403222160…06394317460273238641

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

2.497 × 10¹¹¹(112-digit number)

24974378986806444320…12788634920546477279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.497 × 10¹¹¹(112-digit number)

24974378986806444320…12788634920546477281

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

4.994 × 10¹¹¹(112-digit number)

49948757973612888641…25577269841092954559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.994 × 10¹¹¹(112-digit number)

49948757973612888641…25577269841092954561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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