Block #293,976

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/4/2013, 3:05:41 PM · Difficulty 9.9908 · 6,501,683 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7e89e742a6b992eea92624ce391a1a3dd85455a0261c9543f682e501e61cc49e

View on Chainz ↗

Height

#293,976

Difficulty

9.990835

Transactions

Size

1.18 KB

Version

Bits

09fda75e

Nonce

29,429

Timestamp

12/4/2013, 3:05:41 PM

Confirmations

6,501,683

Mined by

⛏️ X|aRDAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

d6f5c28e2cc06a609119406ad0a268ab01c5ad798f45021dc7a089313398f2ec

Transactions (1)

Coinbased6f5c28e2cc06a…a089313398f2ec

1 in → 31 out9.9800 XPM1.09 KB

APeshfYV…3PKcKMKH AJzWx2VD…j4ZSMit5 AUpEhJju…7ou9xH7C AGD15wje…Q1diJU2D AHuJ9wYh…BGmgHrKZ

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.

2.285 × 10⁹³(94-digit number)

22854741023894093875…47632714314337643559

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

2.285 × 10⁹³(94-digit number)

22854741023894093875…47632714314337643559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.285 × 10⁹³(94-digit number)

22854741023894093875…47632714314337643561

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

4.570 × 10⁹³(94-digit number)

45709482047788187751…95265428628675287119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.570 × 10⁹³(94-digit number)

45709482047788187751…95265428628675287121

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

9.141 × 10⁹³(94-digit number)

91418964095576375502…90530857257350574239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.141 × 10⁹³(94-digit number)

91418964095576375502…90530857257350574241

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

1.828 × 10⁹⁴(95-digit number)

18283792819115275100…81061714514701148479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.828 × 10⁹⁴(95-digit number)

18283792819115275100…81061714514701148481

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

3.656 × 10⁹⁴(95-digit number)

36567585638230550200…62123429029402296959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.656 × 10⁹⁴(95-digit number)

36567585638230550200…62123429029402296961

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