Block #284,105

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 12:30:39 AM · Difficulty 9.9821 · 6,508,479 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

26dd3f023302abe5b40ef8caf6576cc63d45083c455379ef4d23a9add3cedd3d

View on Chainz ↗

Height

#284,105

Difficulty

9.982114

Transactions

Size

24.33 KB

Version

Bits

09fb6bd8

Nonce

606

Timestamp

11/30/2013, 12:30:39 AM

Confirmations

6,508,479

Merkle Root

933354f14a7de0f3be5681cac004f7de690ecd179d11ff7e3cff8a3dc271db81

Transactions (3)

Coinbase9ebc999cf32044…3c582c319ee4c8

1 in → 1 out10.2800 XPM110 B

AeKNrjNj…1NEq95Ta

a94576bf6565e4…8d052c819f72dd

6 in → 2 out24.8000 XPM966 B

AaP3Adcn…4nNKpoCH AV1GRsUG…UgTKm58L

9be24fcfed3e1d…557d98c30d84ec

160 in → 2 out54.0572 XPM23.19 KB

APhZbt91…ERWP9zpq ATELFMa3…TAmdZA4Z

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.

2.615 × 10⁹²(93-digit number)

26154385049516198171…97178755137119288599

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

2.615 × 10⁹²(93-digit number)

26154385049516198171…97178755137119288599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.615 × 10⁹²(93-digit number)

26154385049516198171…97178755137119288601

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

5.230 × 10⁹²(93-digit number)

52308770099032396343…94357510274238577199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.230 × 10⁹²(93-digit number)

52308770099032396343…94357510274238577201

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

1.046 × 10⁹³(94-digit number)

10461754019806479268…88715020548477154399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.046 × 10⁹³(94-digit number)

10461754019806479268…88715020548477154401

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

2.092 × 10⁹³(94-digit number)

20923508039612958537…77430041096954308799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.092 × 10⁹³(94-digit number)

20923508039612958537…77430041096954308801

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

4.184 × 10⁹³(94-digit number)

41847016079225917074…54860082193908617599

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