Block #261,809

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/16/2013, 4:34:41 AM · Difficulty 9.9707 · 6,546,372 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

67b864f8b7b9cf7159e55b88096da67dcf07e4e113d55ad1d180701902473504

View on Chainz ↗

Height

#261,809

Difficulty

9.970657

Transactions

Size

1.64 KB

Version

Bits

09f87cf6

Nonce

213,486

Timestamp

11/16/2013, 4:34:41 AM

Confirmations

6,546,372

Mined by

⛏️ aRAVR2XjZCn2hAXnqkrfFMwQJoCevRB3XTbU

Merkle Root

830e5fe24f93a3050cc6edd2e523806e97729d9c1d0458718cfa5f9041622fc8

Transactions (1)

Coinbase830e5fe24f93a3…fa5f9041622fc8

1 in → 45 out10.0200 XPM1.56 KB

AVR2XjZC…vRB3XTbU APH8rV6F…heb1HF2Z AKXeSXzu…yeuNjvhB AdnG9gQ7…N9B7mA2p AQtzUSwq…htAuF3yC

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.

2.820 × 10⁹⁷(98-digit number)

28201678807836753343…91101962568662865919

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

2.820 × 10⁹⁷(98-digit number)

28201678807836753343…91101962568662865919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.820 × 10⁹⁷(98-digit number)

28201678807836753343…91101962568662865921

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

5.640 × 10⁹⁷(98-digit number)

56403357615673506686…82203925137325731839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.640 × 10⁹⁷(98-digit number)

56403357615673506686…82203925137325731841

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

1.128 × 10⁹⁸(99-digit number)

11280671523134701337…64407850274651463679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.128 × 10⁹⁸(99-digit number)

11280671523134701337…64407850274651463681

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

2.256 × 10⁹⁸(99-digit number)

22561343046269402674…28815700549302927359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.256 × 10⁹⁸(99-digit number)

22561343046269402674…28815700549302927361

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

4.512 × 10⁹⁸(99-digit number)

45122686092538805348…57631401098605854719

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 #261,809

Cookie Preferences