Block #284,390

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 2:50:53 AM · Difficulty 9.9826 · 6,522,839 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cd2035f945913e394a61201afbb39e0281cc5a4fa562011114073f4dd002ae26

View on Chainz ↗

Height

#284,390

Difficulty

9.982634

Transactions

Size

1.18 KB

Version

Bits

09fb8dec

Nonce

97,998

Timestamp

11/30/2013, 2:50:53 AM

Confirmations

6,522,839

Mined by

⛏️ VaRRIAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

08ab94debf6832e25c0a4c4797946e68f05b495a8ddca59d87868b819f777e05

Transactions (1)

Coinbase08ab94debf6832…868b819f777e05

1 in → 31 out10.0000 XPM1.09 KB

AQwRN8bE…V8PsTcY9 APeshfYV…3PKcKMKH AKEwr54i…9BfmMkRh Ae58nAEb…GFUA15fv AXzcEfhQ…Dz9wL2mD

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.

2.762 × 10⁹²(93-digit number)

27627003275583794524…04232182698731059879

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

2.762 × 10⁹²(93-digit number)

27627003275583794524…04232182698731059879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.762 × 10⁹²(93-digit number)

27627003275583794524…04232182698731059881

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

5.525 × 10⁹²(93-digit number)

55254006551167589048…08464365397462119759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.525 × 10⁹²(93-digit number)

55254006551167589048…08464365397462119761

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

1.105 × 10⁹³(94-digit number)

11050801310233517809…16928730794924239519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.105 × 10⁹³(94-digit number)

11050801310233517809…16928730794924239521

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

2.210 × 10⁹³(94-digit number)

22101602620467035619…33857461589848479039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.210 × 10⁹³(94-digit number)

22101602620467035619…33857461589848479041

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

4.420 × 10⁹³(94-digit number)

44203205240934071238…67714923179696958079

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

Block #284,390

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