Block #265,090

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/19/2013, 6:32:21 AM · Difficulty 9.9632 · 6,538,672 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3da4ea81fd0079fb7af042fa2e81f94d5dfa2b5b11e5f175a9bb5b89b76c09ff

View on Chainz ↗

Height

#265,090

Difficulty

9.963208

Transactions

Size

785 B

Version

Bits

09f694c6

Nonce

7,558

Timestamp

11/19/2013, 6:32:21 AM

Confirmations

6,538,672

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

f18e977e9c897beef74913558a4918772c12292f48a15d3a6d8206358b045974

Transactions (2)

Coinbase2833741838394d…ea2bba9c17cfb0

1 in → 2 out10.0800 XPM137 B

AKcbk49N…GJbKa7j1 AKNbfPoc…jfkpwAyL

c544ca56c231b4…ea8323386dcc1f

3 in → 3 out692.9100 XPM556 B

AMZYFYRw…JGLmZSbu ATDg1wpK…dc5kwZ3e ASBsQ9Vr…dZThUadf

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.

3.125 × 10⁹⁸(99-digit number)

31253101913122583414…27466386406283110399

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

3.125 × 10⁹⁸(99-digit number)

31253101913122583414…27466386406283110399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.125 × 10⁹⁸(99-digit number)

31253101913122583414…27466386406283110401

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

6.250 × 10⁹⁸(99-digit number)

62506203826245166829…54932772812566220799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.250 × 10⁹⁸(99-digit number)

62506203826245166829…54932772812566220801

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

1.250 × 10⁹⁹(100-digit number)

12501240765249033365…09865545625132441599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.250 × 10⁹⁹(100-digit number)

12501240765249033365…09865545625132441601

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

2.500 × 10⁹⁹(100-digit number)

25002481530498066731…19731091250264883199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.500 × 10⁹⁹(100-digit number)

25002481530498066731…19731091250264883201

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

5.000 × 10⁹⁹(100-digit number)

50004963060996133463…39462182500529766399

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