Block #321,106

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/20/2013, 2:43:50 AM · Difficulty 10.1868 · 6,489,307 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ff090a5cc18fee9567e9211133d4ba2921f1fe86b81faca29164eca52808317a

View on Chainz ↗

Height

#321,106

Difficulty

10.186840

Transactions

Size

1.95 KB

Version

Bits

0a2fd4c5

Nonce

235,752

Timestamp

12/20/2013, 2:43:50 AM

Confirmations

6,489,307

Mined by

⛏️ RaRKAc6mGvmQ9ya8dQxqWNQYGz81U4XqWmPHjR

Merkle Root

9bbac8f72b423ee666cb61169f64343cb7033a32a14453fcca96dc2617f338a6

Transactions (4)

Coinbase399ba8fc8106c8…838e55855aceb7

1 in → 21 out9.6200 XPM777 B

Ac6mGvmQ…XqWmPHjR Aac9Hjdg…P4ktypc3 AP5UvYhU…vLTDwkdA AU1TRxZz…petNoBtK Ad9pSzHt…cpJ3y2zz

f34b417e5f35fc…3c7286637ab62f

4 in → 2 out12.2874 XPM672 B

AMaNVBkH…if7A3Urp AZvfusHN…W8ccC5r1

727efe593a1bce…10843c63f3b97c

1 in → 2 out7.6484 XPM227 B

AQH5ZHnG…X3F7vpCH AYFxzicp…jeAdgy2P

ca560ed84f1df0…5d1c3a353fcaea

1 in → 2 out1.3993 XPM225 B

Acr57bhu…h8nSyey8 AMMJb1y3…VPoDQv6m

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.

9.258 × 10⁹⁹(100-digit number)

92589061555068671954…12343238960678648959

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

9.258 × 10⁹⁹(100-digit number)

92589061555068671954…12343238960678648959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.258 × 10⁹⁹(100-digit number)

92589061555068671954…12343238960678648961

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

1.851 × 10¹⁰⁰(101-digit number)

18517812311013734390…24686477921357297919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.851 × 10¹⁰⁰(101-digit number)

18517812311013734390…24686477921357297921

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

3.703 × 10¹⁰⁰(101-digit number)

37035624622027468781…49372955842714595839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.703 × 10¹⁰⁰(101-digit number)

37035624622027468781…49372955842714595841

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

7.407 × 10¹⁰⁰(101-digit number)

74071249244054937563…98745911685429191679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.407 × 10¹⁰⁰(101-digit number)

74071249244054937563…98745911685429191681

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

1.481 × 10¹⁰¹(102-digit number)

14814249848810987512…97491823370858383359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.481 × 10¹⁰¹(102-digit number)

14814249848810987512…97491823370858383361

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

Block #321,106

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