Block #221,474

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 2:29:46 PM · Difficulty 9.9390 · 6,604,222 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ba28d9c945ebf0fe3e7d1a44f0a4b46b49f5d36f17f9a1f1796a2d9cc4b02345

View on Chainz ↗

Height

#221,474

Difficulty

9.938971

Transactions

Size

38.30 KB

Version

Bits

09f06069

Nonce

11,640

Timestamp

10/21/2013, 2:29:46 PM

Confirmations

6,604,222

Mined by

⛏️ P2SHAMvWpNL8qJvbpRY6cXnA4fQZiaiTY6SCP1

Merkle Root

0891b78ab75226809a638580c343205d41be98bca201f6e35fe5165e2f10f555

Transactions (2)

Coinbase813f327cf4c5b7…67acf7ed9fb92c

1 in → 1 out10.5100 XPM109 B

AMvWpNL8…iTY6SCP1

6a3e4b4e54e5cb…cee751380be376

263 in → 2 out100.0100 XPM38.11 KB

AQkvZEnd…pftRkZHB AYjYMQg5…eSw6jJor

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.

1.284 × 10⁹⁵(96-digit number)

12844699256526070714…81977872277461952479

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

1.284 × 10⁹⁵(96-digit number)

12844699256526070714…81977872277461952479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.284 × 10⁹⁵(96-digit number)

12844699256526070714…81977872277461952481

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

2.568 × 10⁹⁵(96-digit number)

25689398513052141429…63955744554923904959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.568 × 10⁹⁵(96-digit number)

25689398513052141429…63955744554923904961

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

5.137 × 10⁹⁵(96-digit number)

51378797026104282859…27911489109847809919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.137 × 10⁹⁵(96-digit number)

51378797026104282859…27911489109847809921

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

1.027 × 10⁹⁶(97-digit number)

10275759405220856571…55822978219695619839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.027 × 10⁹⁶(97-digit number)

10275759405220856571…55822978219695619841

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

2.055 × 10⁹⁶(97-digit number)

20551518810441713143…11645956439391239679

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 #221,474

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