Block #222,439

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/22/2013, 5:59:43 AM · Difficulty 9.9394 · 6,580,706 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b5b6a0df59d3937a3d86472be8644f5d3f7aa4175decda811b28accaa90eadf8

View on Chainz ↗

Height

#222,439

Difficulty

9.939378

Transactions

Size

1.10 KB

Version

Bits

09f07b1b

Nonce

120,459

Timestamp

10/22/2013, 5:59:43 AM

Confirmations

6,580,706

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

0036c801e65dd14b3a983dd05a4816c7a4ed158d035e3a1d2750eeb8e330b2a8

Transactions (3)

Coinbaseb781d4039aba6c…bf8ace457478cb

1 in → 1 out10.1300 XPM110 B

AbuU1HhS…JPwsJEbB

b36295ac61df76…baca0f8385f679

4 in → 7 out40.4700 XPM705 B

AbuU1HhS…JPwsJEbB AddYPtQ7…r1XeEMSA Ac83zZ3S…ipFefqdu Abu1uzTT…6jPtvXzW AcyPVp7N…dDULWcdA

b731e22b9f9c56…53793948948161

1 in → 2 out6.9675 XPM226 B

AQAUtWX9…Uub8YSx5 AUUJC7ne…cmZaPWM6

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.

2.717 × 10⁹³(94-digit number)

27179708375045089527…45987895606900150289

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

2.717 × 10⁹³(94-digit number)

27179708375045089527…45987895606900150289

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.717 × 10⁹³(94-digit number)

27179708375045089527…45987895606900150291

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

5.435 × 10⁹³(94-digit number)

54359416750090179055…91975791213800300579

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.435 × 10⁹³(94-digit number)

54359416750090179055…91975791213800300581

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

1.087 × 10⁹⁴(95-digit number)

10871883350018035811…83951582427600601159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.087 × 10⁹⁴(95-digit number)

10871883350018035811…83951582427600601161

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

2.174 × 10⁹⁴(95-digit number)

21743766700036071622…67903164855201202319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.174 × 10⁹⁴(95-digit number)

21743766700036071622…67903164855201202321

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

4.348 × 10⁹⁴(95-digit number)

43487533400072143244…35806329710402404639

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