Block #242,991

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 1:15:45 AM · Difficulty 9.9608 · 6,555,598 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0785cc0922d07aea913e0e446178ae98ab897fa97a08f589d1e6a19cf0ca363a

View on Chainz ↗

Height

#242,991

Difficulty

9.960845

Transactions

Size

652 B

Version

Bits

09f5f9ed

Nonce

298,250

Timestamp

11/4/2013, 1:15:45 AM

Confirmations

6,555,598

Mined by

⛏️ P2SHAduwQQFvXVbJc63VcTAzaevCj5XRuPt4i8

Merkle Root

c29f50b5ca56f92f49d6b5c720fb5e92f038520babe755abf869bd70239ed7e9

Transactions (3)

Coinbasec3ead5f3912412…a2d963698e45d7

1 in → 1 out10.0800 XPM109 B

AduwQQFv…XRuPt4i8

8571671f15bd0a…3fa41c5f135d60

1 in → 4 out10.0700 XPM261 B

AeKNrjNj…1NEq95Ta Ac52HjfZ…tL3Rs7Sd APunRQdW…d1sQ4Mjp AcyPVp7N…dDULWcdA

9030bef62febf0…7320f66f24e88d

1 in → 1 out13.1495 XPM192 B

AXhMcKBp…Drzdc8Hw

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.

1.238 × 10⁹⁵(96-digit number)

12387866692423528089…91018299223278291199

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

1.238 × 10⁹⁵(96-digit number)

12387866692423528089…91018299223278291199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.238 × 10⁹⁵(96-digit number)

12387866692423528089…91018299223278291201

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

2.477 × 10⁹⁵(96-digit number)

24775733384847056178…82036598446556582399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.477 × 10⁹⁵(96-digit number)

24775733384847056178…82036598446556582401

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

4.955 × 10⁹⁵(96-digit number)

49551466769694112357…64073196893113164799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.955 × 10⁹⁵(96-digit number)

49551466769694112357…64073196893113164801

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

9.910 × 10⁹⁵(96-digit number)

99102933539388224714…28146393786226329599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.910 × 10⁹⁵(96-digit number)

99102933539388224714…28146393786226329601

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

1.982 × 10⁹⁶(97-digit number)

19820586707877644942…56292787572452659199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.982 × 10⁹⁶(97-digit number)

19820586707877644942…56292787572452659201

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