Block #261,433

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/15/2013, 5:24:54 PM · Difficulty 9.9723 · 6,551,611 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c0c8924a101beff6c0703d964818f675ab9f3bfd5a2c957e2277e6a990b831e0

View on Chainz ↗

Height

#261,433

Difficulty

9.972306

Transactions

Size

600 B

Version

Bits

09f8e910

Nonce

14,311

Timestamp

11/15/2013, 5:24:54 PM

Confirmations

6,551,611

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

4c5857aa6d2381c59fc7e6760cd145bc9eafa848ea307a753942794233ae9b19

Transactions (2)

Coinbase29834ec2de7cd8…46f9c32355ed51

1 in → 2 out10.0500 XPM137 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

5300b5671b762e…d2b24662e2bbcc

2 in → 2 out1.0135 XPM373 B

AFqvL2G8…stXLaJty AXCtMxXM…A168QgUA

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.

1.532 × 10⁹⁴(95-digit number)

15328432972551970410…15895556182573683199

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

1.532 × 10⁹⁴(95-digit number)

15328432972551970410…15895556182573683199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.532 × 10⁹⁴(95-digit number)

15328432972551970410…15895556182573683201

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

3.065 × 10⁹⁴(95-digit number)

30656865945103940821…31791112365147366399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.065 × 10⁹⁴(95-digit number)

30656865945103940821…31791112365147366401

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

6.131 × 10⁹⁴(95-digit number)

61313731890207881642…63582224730294732799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.131 × 10⁹⁴(95-digit number)

61313731890207881642…63582224730294732801

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

1.226 × 10⁹⁵(96-digit number)

12262746378041576328…27164449460589465599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.226 × 10⁹⁵(96-digit number)

12262746378041576328…27164449460589465601

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

2.452 × 10⁹⁵(96-digit number)

24525492756083152656…54328898921178931199

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

Block #261,433

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