Block #302,092

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/9/2013, 3:01:56 PM · Difficulty 9.9926 · 6,501,231 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f1205210be284bcd4a8d82ab2ca48524a92e7e9e301dd6c5023fd7d0eff98c14

View on Chainz ↗

Height

#302,092

Difficulty

9.992620

Transactions

Size

1.18 KB

Version

Bits

09fe1c52

Nonce

9,131

Timestamp

12/9/2013, 3:01:56 PM

Confirmations

6,501,231

Mined by

⛏️ aRkAWZd1qVJsLEYJ7QkpZDB3cXqFz9pj9yfPa

Merkle Root

e543afe937862f91c4c93ee09aa4e63d9acc67da0a7cdcb21a9d222cf2b02ba9

Transactions (1)

Coinbasee543afe937862f…9d222cf2b02ba9

1 in → 31 out9.9800 XPM1.09 KB

AWZd1qVJ…9pj9yfPa AHuJ9wYh…BGmgHrKZ ARcqMJhp…RVLToQ6S AXNGJQx4…d9FM96S4 AFyxqNLu…Sa9m9dGK

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.

6.559 × 10⁹³(94-digit number)

65590647007577729942…86560744678996121599

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

6.559 × 10⁹³(94-digit number)

65590647007577729942…86560744678996121599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.559 × 10⁹³(94-digit number)

65590647007577729942…86560744678996121601

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

1.311 × 10⁹⁴(95-digit number)

13118129401515545988…73121489357992243199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.311 × 10⁹⁴(95-digit number)

13118129401515545988…73121489357992243201

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

2.623 × 10⁹⁴(95-digit number)

26236258803031091977…46242978715984486399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.623 × 10⁹⁴(95-digit number)

26236258803031091977…46242978715984486401

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

5.247 × 10⁹⁴(95-digit number)

52472517606062183954…92485957431968972799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.247 × 10⁹⁴(95-digit number)

52472517606062183954…92485957431968972801

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

1.049 × 10⁹⁵(96-digit number)

10494503521212436790…84971914863937945599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.049 × 10⁹⁵(96-digit number)

10494503521212436790…84971914863937945601

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