Block #237,042

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 7:46:17 PM · Difficulty 9.9490 · 6,567,020 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

850940ac7daa96514e51f5525fdafa9aa79590b913fee3b98b1186f482f84fa1

View on Chainz ↗

Height

#237,042

Difficulty

9.948992

Transactions

Size

1.54 KB

Version

Bits

09f2f12b

Nonce

12,777

Timestamp

10/31/2013, 7:46:17 PM

Confirmations

6,567,020

Mined by

⛏️ RrAMttQDuftdpMyrb199TXiUSH5L7j6tfS9x

Merkle Root

142ceac1959c7e4f1f266f727fe5622e777d5fb3b63ac1ab565d0992e6e9d0da

Transactions (1)

Coinbase142ceac1959c7e…5d0992e6e9d0da

1 in → 42 out10.0700 XPM1.46 KB

AMttQDuf…7j6tfS9x AbeUZSvK…ijGzuyjz AdnG9gQ7…N9B7mA2p AQtzUSwq…htAuF3yC AcEnwywz…vZtt2xTs

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.

2.286 × 10⁹⁴(95-digit number)

22864826194957540561…06453372469017538559

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

2.286 × 10⁹⁴(95-digit number)

22864826194957540561…06453372469017538559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.286 × 10⁹⁴(95-digit number)

22864826194957540561…06453372469017538561

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

4.572 × 10⁹⁴(95-digit number)

45729652389915081123…12906744938035077119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.572 × 10⁹⁴(95-digit number)

45729652389915081123…12906744938035077121

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

9.145 × 10⁹⁴(95-digit number)

91459304779830162247…25813489876070154239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.145 × 10⁹⁴(95-digit number)

91459304779830162247…25813489876070154241

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

1.829 × 10⁹⁵(96-digit number)

18291860955966032449…51626979752140308479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.829 × 10⁹⁵(96-digit number)

18291860955966032449…51626979752140308481

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

3.658 × 10⁹⁵(96-digit number)

36583721911932064898…03253959504280616959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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