Block #323,696

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/21/2013, 7:56:39 PM · Difficulty 10.2061 · 6,471,066 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7ce46f19df30fe530e0d5d196e4eb9a59ef7f6666c037a582a1f2d3d84a83bff

View on Chainz ↗

Height

#323,696

Difficulty

10.206112

Transactions

Size

1.01 KB

Version

Bits

0a34c3be

Nonce

290,575

Timestamp

12/21/2013, 7:56:39 PM

Confirmations

6,471,066

Mined by

⛏️ paR1AQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

e08eac9115f1449093869b47ba04bad99097aa22a6fe47937961c8161bc861c5

Transactions (1)

Coinbasee08eac9115f144…61c8161bc861c5

1 in → 26 out9.5900 XPM947 B

AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz AG5YAjec…VhA4Aeh1

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.

8.227 × 10⁹⁹(100-digit number)

82272437392568998521…50743767944087190689

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

8.227 × 10⁹⁹(100-digit number)

82272437392568998521…50743767944087190689

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.227 × 10⁹⁹(100-digit number)

82272437392568998521…50743767944087190691

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

1.645 × 10¹⁰⁰(101-digit number)

16454487478513799704…01487535888174381379

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.645 × 10¹⁰⁰(101-digit number)

16454487478513799704…01487535888174381381

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

3.290 × 10¹⁰⁰(101-digit number)

32908974957027599408…02975071776348762759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.290 × 10¹⁰⁰(101-digit number)

32908974957027599408…02975071776348762761

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

6.581 × 10¹⁰⁰(101-digit number)

65817949914055198817…05950143552697525519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.581 × 10¹⁰⁰(101-digit number)

65817949914055198817…05950143552697525521

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

1.316 × 10¹⁰¹(102-digit number)

13163589982811039763…11900287105395051039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.316 × 10¹⁰¹(102-digit number)

13163589982811039763…11900287105395051041

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