Block #8,002

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/10/2013, 1:33:08 PM · Difficulty 7.5465 · 6,781,073 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

69492d4fce55931c7e3f109bf50a95a64b8b6724d0f96a134ea23a9edadb6014

View on Chainz ↗

Height

#8,002

Difficulty

7.546492

Transactions

Size

2.94 KB

Version

Bits

078be6e9

Nonce

162

Timestamp

7/10/2013, 1:33:08 PM

Confirmations

6,781,073

Merkle Root

62e9d74aac8264f76c9368d73b3bc12de3fb6db3d3e1adc3f1c579cd204ab4ec

Transactions (3)

Coinbase5809c7c1f4be5e…cb3670a9d72a3c

1 in → 1 out17.5800 XPM108 B

AYjt3DSx…WufHisFn

d40193fd6c9b5a…6c44fee973e0cc

17 in → 2 out334.0300 XPM2.00 KB

AJadurLR…imGxDjiF AUCN9bSu…wxCjUfzG

0ee6e5b021806d…e3baab791dd520

6 in → 2 out114.1000 XPM762 B

AJNyv44i…z4zNEHHy ASbwQVgn…3NEZCiVS

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.

9.203 × 10⁹⁴(95-digit number)

92031389276727047050…90764935363887903639

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

9.203 × 10⁹⁴(95-digit number)

92031389276727047050…90764935363887903639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.203 × 10⁹⁴(95-digit number)

92031389276727047050…90764935363887903641

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

1.840 × 10⁹⁵(96-digit number)

18406277855345409410…81529870727775807279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.840 × 10⁹⁵(96-digit number)

18406277855345409410…81529870727775807281

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

3.681 × 10⁹⁵(96-digit number)

36812555710690818820…63059741455551614559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.681 × 10⁹⁵(96-digit number)

36812555710690818820…63059741455551614561

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

7.362 × 10⁹⁵(96-digit number)

73625111421381637640…26119482911103229119

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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