Block #266,000

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/20/2013, 2:18:40 AM · Difficulty 9.9612 · 6,526,746 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f403b3b43512928a3ea22eb3fb50ec09e44b6cfad65dec9d644102bacd2ff7d9

View on Chainz ↗

Height

#266,000

Difficulty

9.961173

Transactions

Size

607 B

Version

Bits

09f60f72

Nonce

7,376

Timestamp

11/20/2013, 2:18:40 AM

Confirmations

6,526,746

Merkle Root

07c5dd71c9690b2075ad3a56716912bc6cd816d6e0f7f3cad188efe10f5a1872

Transactions (2)

Coinbasec9e780e2931790…43148b55354849

1 in → 2 out10.0700 XPM142 B

AdGRRh1e…QmctLb24 AKNbfPoc…jfkpwAyL

0947533d9387e6…a68d7fd5dd0aa1

2 in → 2 out2.0244 XPM374 B

AMJDChGB…VXxUjXFK AXAxEoWg…Aebxe4sR

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.

1.339 × 10⁹⁸(99-digit number)

13394132848303693007…07501322001550279699

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

1.339 × 10⁹⁸(99-digit number)

13394132848303693007…07501322001550279699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.339 × 10⁹⁸(99-digit number)

13394132848303693007…07501322001550279701

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

2.678 × 10⁹⁸(99-digit number)

26788265696607386015…15002644003100559399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.678 × 10⁹⁸(99-digit number)

26788265696607386015…15002644003100559401

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

5.357 × 10⁹⁸(99-digit number)

53576531393214772031…30005288006201118799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.357 × 10⁹⁸(99-digit number)

53576531393214772031…30005288006201118801

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

1.071 × 10⁹⁹(100-digit number)

10715306278642954406…60010576012402237599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.071 × 10⁹⁹(100-digit number)

10715306278642954406…60010576012402237601

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

2.143 × 10⁹⁹(100-digit number)

21430612557285908812…20021152024804475199

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