Block #221,173

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 10:34:26 AM · Difficulty 9.9382 · 6,588,411 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7de5b126d8e9b4a0aa0d58df7d35da739515282d1800489f8884b9b9ac995e3e

View on Chainz ↗

Height

#221,173

Difficulty

9.938168

Transactions

Size

583 B

Version

Bits

09f02bcb

Nonce

36,716

Timestamp

10/21/2013, 10:34:26 AM

Confirmations

6,588,411

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

8c01ce1f86dd3bfe46f957920cf8081058e55872829cb9b923b3515ba53ea686

Transactions (3)

Coinbase1c7afde8a46337…a45b92a45dcad5

1 in → 1 out10.1300 XPM110 B

AbuU1HhS…JPwsJEbB

52b8e12cb3b334…3932ba06cf9ac2

1 in → 1 out10.1400 XPM158 B

ATV4M1CV…dd9zw8nH

c218b828018bc5…2952a71763c371

1 in → 3 out10.1600 XPM225 B

AcADmAoe…8iNnoMzB AbuU1HhS…JPwsJEbB AHLyZUb7…cHnQjZJ9

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.

2.982 × 10⁹⁴(95-digit number)

29826036466066543393…56946501229335823039

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

2.982 × 10⁹⁴(95-digit number)

29826036466066543393…56946501229335823039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.982 × 10⁹⁴(95-digit number)

29826036466066543393…56946501229335823041

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

5.965 × 10⁹⁴(95-digit number)

59652072932133086787…13893002458671646079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.965 × 10⁹⁴(95-digit number)

59652072932133086787…13893002458671646081

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

1.193 × 10⁹⁵(96-digit number)

11930414586426617357…27786004917343292159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.193 × 10⁹⁵(96-digit number)

11930414586426617357…27786004917343292161

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

2.386 × 10⁹⁵(96-digit number)

23860829172853234715…55572009834686584319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.386 × 10⁹⁵(96-digit number)

23860829172853234715…55572009834686584321

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

4.772 × 10⁹⁵(96-digit number)

47721658345706469430…11144019669373168639

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

Block #221,173

Cookie Preferences