Block #221,432

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 2:00:10 PM · Difficulty 9.9388 · 6,591,107 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f6d807fabff7dbec0631b3293d5f8f3d034633fd01473ad611793b2796da54ef

View on Chainz ↗

Height

#221,432

Difficulty

9.938836

Transactions

Size

1.44 KB

Version

Bits

09f05792

Nonce

7,921

Timestamp

10/21/2013, 2:00:10 PM

Confirmations

6,591,107

Mined by

⛏️ P2SHAWscwrCfzY4KJfxQpZFN3j4torNvepQkLX

Merkle Root

22c9cb89a165918fde2c545ef3714c2cefa44a57a0966493ef259df091fd5a00

Transactions (3)

Coinbase3d1cece5f2a6e5…7f31f2c05cf1ad

1 in → 1 out10.1400 XPM109 B

AWscwrCf…NvepQkLX

9570e374ad6b02…515cc4b5e31eaa

1 in → 2 out10.1200 XPM226 B

ATBkKaHF…pZfkynuT ALL6BtTJ…cp6j3qpk

3bc9b6c586cfb9…8ebab55df8a5a1

7 in → 2 out21.0300 XPM1.02 KB

AFz9fXym…wh4UqpkL AYW7enLM…HGRJriPk

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.

4.915 × 10⁹⁸(99-digit number)

49153443882151123763…39306228114928089599

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

4.915 × 10⁹⁸(99-digit number)

49153443882151123763…39306228114928089599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.915 × 10⁹⁸(99-digit number)

49153443882151123763…39306228114928089601

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

9.830 × 10⁹⁸(99-digit number)

98306887764302247527…78612456229856179199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.830 × 10⁹⁸(99-digit number)

98306887764302247527…78612456229856179201

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

1.966 × 10⁹⁹(100-digit number)

19661377552860449505…57224912459712358399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.966 × 10⁹⁹(100-digit number)

19661377552860449505…57224912459712358401

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

3.932 × 10⁹⁹(100-digit number)

39322755105720899010…14449824919424716799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.932 × 10⁹⁹(100-digit number)

39322755105720899010…14449824919424716801

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

7.864 × 10⁹⁹(100-digit number)

78645510211441798021…28899649838849433599

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 #221,432

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