Block #323,210

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/21/2013, 12:14:41 PM · Difficulty 10.2023 · 6,472,419 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5b1af3de25edb94088ae9a3f99bbf0fb2843f4ed5724402b2d86d772539ddea3

View on Chainz ↗

Height

#323,210

Difficulty

10.202334

Transactions

Size

1.05 KB

Version

Bits

0a33cc25

Nonce

49,515

Timestamp

12/21/2013, 12:14:41 PM

Confirmations

6,472,419

Mined by

⛏️ aR;Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

0c988894d97105b694f3624f48fb99d378c9ca7b4284d6d5553335f7faa274ab

Transactions (1)

Coinbase0c988894d97105…3335f7faa274ab

1 in → 27 out9.5900 XPM981 B

Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz AQ8QAT3J…rCFKuVbR AKzkYQaQ…zR4FspJZ Ae58nAEb…GFUA15fv

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.

1.181 × 10⁹⁸(99-digit number)

11818088750143264067…78099760797319502079

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

1.181 × 10⁹⁸(99-digit number)

11818088750143264067…78099760797319502079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.181 × 10⁹⁸(99-digit number)

11818088750143264067…78099760797319502081

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

2.363 × 10⁹⁸(99-digit number)

23636177500286528134…56199521594639004159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.363 × 10⁹⁸(99-digit number)

23636177500286528134…56199521594639004161

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

4.727 × 10⁹⁸(99-digit number)

47272355000573056268…12399043189278008319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.727 × 10⁹⁸(99-digit number)

47272355000573056268…12399043189278008321

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

9.454 × 10⁹⁸(99-digit number)

94544710001146112537…24798086378556016639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.454 × 10⁹⁸(99-digit number)

94544710001146112537…24798086378556016641

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

1.890 × 10⁹⁹(100-digit number)

18908942000229222507…49596172757112033279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.890 × 10⁹⁹(100-digit number)

18908942000229222507…49596172757112033281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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