Block #334,895

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/29/2013, 7:44:14 PM · Difficulty 10.1593 · 6,475,516 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7ee5fac3803550b43bd84b4c1010c89872a6ae2fd08990780c7db14405059ccd

View on Chainz ↗

Height

#334,895

Difficulty

10.159328

Transactions

Size

1.08 KB

Version

Bits

0a28c9bc

Nonce

2,758

Timestamp

12/29/2013, 7:44:14 PM

Confirmations

6,475,516

Mined by

⛏️ aR{FAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

1e80f9edbaaccfbfc966d1baf8519bd0922b5acf64feca850f5604f5f21750b0

Transactions (1)

Coinbase1e80f9edbaaccf…5604f5f21750b0

1 in → 28 out9.6500 XPM1015 B

AQwRN8bE…V8PsTcY9 AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7

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.

2.223 × 10⁹⁸(99-digit number)

22231206796275937619…93864701841404112539

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

2.223 × 10⁹⁸(99-digit number)

22231206796275937619…93864701841404112539

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.223 × 10⁹⁸(99-digit number)

22231206796275937619…93864701841404112541

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

4.446 × 10⁹⁸(99-digit number)

44462413592551875239…87729403682808225079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.446 × 10⁹⁸(99-digit number)

44462413592551875239…87729403682808225081

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

8.892 × 10⁹⁸(99-digit number)

88924827185103750479…75458807365616450159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.892 × 10⁹⁸(99-digit number)

88924827185103750479…75458807365616450161

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

1.778 × 10⁹⁹(100-digit number)

17784965437020750095…50917614731232900319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.778 × 10⁹⁹(100-digit number)

17784965437020750095…50917614731232900321

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

3.556 × 10⁹⁹(100-digit number)

35569930874041500191…01835229462465800639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.556 × 10⁹⁹(100-digit number)

35569930874041500191…01835229462465800641

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 #334,895

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