Block #235,693

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 2:21:00 AM · Difficulty 9.9458 · 6,570,274 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

72f88c28182a8d3a7eb2faebb9b13625d993fe794e9ba73d0689099b10d7ef8c

View on Chainz ↗

Height

#235,693

Difficulty

9.945810

Transactions

Size

2.21 KB

Version

Bits

09f22094

Nonce

520

Timestamp

10/31/2013, 2:21:00 AM

Confirmations

6,570,274

Mined by

⛏️ RqAdwTEXyCNzh2EiHyiAUCrCetZcNwbVbqZV

Merkle Root

08a980685a89485a3a448ae4634707478f8ce8cfc874bad79601b9197c2e0ba4

Transactions (1)

Coinbase08a980685a8948…01b9197c2e0ba4

1 in → 62 out10.0600 XPM2.12 KB

AdwTEXyC…NwbVbqZV AdnG9gQ7…N9B7mA2p ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AQZYfdBZ…DVLcLRg8

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.

4.941 × 10¹⁰⁰(101-digit number)

49416086675231853388…34830875115713986559

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

4.941 × 10¹⁰⁰(101-digit number)

49416086675231853388…34830875115713986559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.941 × 10¹⁰⁰(101-digit number)

49416086675231853388…34830875115713986561

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

9.883 × 10¹⁰⁰(101-digit number)

98832173350463706776…69661750231427973119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.883 × 10¹⁰⁰(101-digit number)

98832173350463706776…69661750231427973121

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

1.976 × 10¹⁰¹(102-digit number)

19766434670092741355…39323500462855946239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.976 × 10¹⁰¹(102-digit number)

19766434670092741355…39323500462855946241

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

3.953 × 10¹⁰¹(102-digit number)

39532869340185482710…78647000925711892479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.953 × 10¹⁰¹(102-digit number)

39532869340185482710…78647000925711892481

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

7.906 × 10¹⁰¹(102-digit number)

79065738680370965421…57294001851423784959

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