Block #321,226

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/20/2013, 4:38:59 AM · Difficulty 10.1875 · 6,483,859 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

36bf8bc9bc0eaf68908fe896014f388c8f297970e099583621a31d0986dbb00f

View on Chainz ↗

Height

#321,226

Difficulty

10.187527

Transactions

Size

1.08 KB

Version

Bits

0a3001c5

Nonce

2,468

Timestamp

12/20/2013, 4:38:59 AM

Confirmations

6,483,859

Mined by

⛏️ aRkAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

2a0d33e8325df2ea959c251fc6bba30b887c905bf3d294f25c3df6e3925f561f

Transactions (1)

Coinbase2a0d33e8325df2…3df6e3925f561f

1 in → 28 out9.6000 XPM1015 B

Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz AZemWJAo…6jhDtieG AQ8QAT3J…rCFKuVbR AdwTEXyC…NwbVbqZV

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.

7.251 × 10⁹⁷(98-digit number)

72516224940380178766…80670144268960993279

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

7.251 × 10⁹⁷(98-digit number)

72516224940380178766…80670144268960993279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.251 × 10⁹⁷(98-digit number)

72516224940380178766…80670144268960993281

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

1.450 × 10⁹⁸(99-digit number)

14503244988076035753…61340288537921986559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.450 × 10⁹⁸(99-digit number)

14503244988076035753…61340288537921986561

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

2.900 × 10⁹⁸(99-digit number)

29006489976152071506…22680577075843973119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.900 × 10⁹⁸(99-digit number)

29006489976152071506…22680577075843973121

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

5.801 × 10⁹⁸(99-digit number)

58012979952304143013…45361154151687946239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.801 × 10⁹⁸(99-digit number)

58012979952304143013…45361154151687946241

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

1.160 × 10⁹⁹(100-digit number)

11602595990460828602…90722308303375892479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.160 × 10⁹⁹(100-digit number)

11602595990460828602…90722308303375892481

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