Block #52,845

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/16/2013, 12:27:04 PM · Difficulty 8.9169 · 6,743,715 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bceacabf4461614efd359f77021f45e69d99dc31fe4fdc4df332fe71ac24cf16

View on Chainz ↗

Height

#52,845

Difficulty

8.916879

Transactions

Size

359 B

Version

Bits

08eab896

Nonce

1,045

Timestamp

7/16/2013, 12:27:04 PM

Confirmations

6,743,715

Mined by

⛏️ P2SHAK3X8M4n8p5BPtkuFf8v6T3hAuzFeMdGCF

Merkle Root

c871074f470b99d813bacdbb16c9a6f6f546dd5119ceb1c3fe078e5b979b4a4a

Transactions (2)

Coinbase077abd7ce2e49d…ece3891322fa38

1 in → 1 out12.5700 XPM110 B

AK3X8M4n…zFeMdGCF

f902851a7814e0…98b3ebf1eae9c0

1 in → 1 out12.7200 XPM158 B

AFqbAUg8…usozGxmw

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.

1.782 × 10⁹⁸(99-digit number)

17828811436245213412…84258908271140343789

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

1.782 × 10⁹⁸(99-digit number)

17828811436245213412…84258908271140343789

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.782 × 10⁹⁸(99-digit number)

17828811436245213412…84258908271140343791

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

3.565 × 10⁹⁸(99-digit number)

35657622872490426825…68517816542280687579

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.565 × 10⁹⁸(99-digit number)

35657622872490426825…68517816542280687581

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

7.131 × 10⁹⁸(99-digit number)

71315245744980853650…37035633084561375159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.131 × 10⁹⁸(99-digit number)

71315245744980853650…37035633084561375161

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

1.426 × 10⁹⁹(100-digit number)

14263049148996170730…74071266169122750319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.426 × 10⁹⁹(100-digit number)

14263049148996170730…74071266169122750321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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