Block #307,325

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 12:22:57 PM · Difficulty 9.9942 · 6,503,367 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0be884f96d4d60cfe5785f563c75d71976ee35d0a1a9e33d21cb99474af7bbf4

View on Chainz ↗

Height

#307,325

Difficulty

9.994183

Transactions

Size

970 B

Version

Bits

09fe82bf

Nonce

9,932

Timestamp

12/12/2013, 12:22:57 PM

Confirmations

6,503,367

Mined by

⛏️ }aR'Ad9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

e665461614aff840299c2f7f06325d247e937836fc71c5bbdf1387734a5b11bb

Transactions (1)

Coinbasee665461614aff8…1387734a5b11bb

1 in → 24 out10.0000 XPM879 B

Ad9pSzHt…cpJ3y2zz ASWX42VM…XypQABkY AHuJ9wYh…BGmgHrKZ AG5YAjec…VhA4Aeh1 AZ2pPuKg…95SN2Yr7

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.

3.028 × 10⁹⁷(98-digit number)

30285221660690790671…96765216347008184319

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

3.028 × 10⁹⁷(98-digit number)

30285221660690790671…96765216347008184319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.028 × 10⁹⁷(98-digit number)

30285221660690790671…96765216347008184321

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

6.057 × 10⁹⁷(98-digit number)

60570443321381581343…93530432694016368639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.057 × 10⁹⁷(98-digit number)

60570443321381581343…93530432694016368641

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

1.211 × 10⁹⁸(99-digit number)

12114088664276316268…87060865388032737279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.211 × 10⁹⁸(99-digit number)

12114088664276316268…87060865388032737281

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

2.422 × 10⁹⁸(99-digit number)

24228177328552632537…74121730776065474559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.422 × 10⁹⁸(99-digit number)

24228177328552632537…74121730776065474561

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

4.845 × 10⁹⁸(99-digit number)

48456354657105265074…48243461552130949119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.845 × 10⁹⁸(99-digit number)

48456354657105265074…48243461552130949121

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

Block #307,325

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