Block #221,349

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 1:01:03 PM · Difficulty 9.9385 · 6,592,873 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

846d5ed78e4756d62aff68fed870c14f62a6728a805e085754dcd5ad8d29ce55

View on Chainz ↗

Height

#221,349

Difficulty

9.938533

Transactions

Size

1.54 KB

Version

Bits

09f043ac

Nonce

17,892

Timestamp

10/21/2013, 1:01:03 PM

Confirmations

6,592,873

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

034756aa0534768231d030ad94f6a997b1602ae1526c66e2253ba53bcf9e136a

Transactions (2)

Coinbasef913320373bf5e…3dc8cb52c985ab

1 in → 1 out10.1300 XPM110 B

AbuU1HhS…JPwsJEbB

c7ba44dd18e29b…fb5547a83504dc

9 in → 1 out199.9900 XPM1.35 KB

AbzpjPEq…whhdA9w7

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.

1.342 × 10⁹⁴(95-digit number)

13420901841918523517…30059467564003746719

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

1.342 × 10⁹⁴(95-digit number)

13420901841918523517…30059467564003746719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.342 × 10⁹⁴(95-digit number)

13420901841918523517…30059467564003746721

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

2.684 × 10⁹⁴(95-digit number)

26841803683837047034…60118935128007493439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.684 × 10⁹⁴(95-digit number)

26841803683837047034…60118935128007493441

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

5.368 × 10⁹⁴(95-digit number)

53683607367674094069…20237870256014986879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.368 × 10⁹⁴(95-digit number)

53683607367674094069…20237870256014986881

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

1.073 × 10⁹⁵(96-digit number)

10736721473534818813…40475740512029973759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.073 × 10⁹⁵(96-digit number)

10736721473534818813…40475740512029973761

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

2.147 × 10⁹⁵(96-digit number)

21473442947069637627…80951481024059947519

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 #221,349

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