Block #212,590

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/16/2013, 9:30:03 AM · Difficulty 9.9191 · 6,588,965 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c6219fc278ffcc36638aec9abdcf49bfe44b7bd894826864d17ef903a8d9d01c

View on Chainz ↗

Height

#212,590

Difficulty

9.919075

Transactions

Size

1.61 KB

Version

Bits

09eb4887

Nonce

25,722

Timestamp

10/16/2013, 9:30:03 AM

Confirmations

6,588,965

Mined by

⛏️ P2SHAd786hwVrw2jz1B5De2ScfExLQM41PPm9x

Merkle Root

dd6de77c33314659fb7e1928ad7755b395d412b6df8375eaec0c1641d32eeaaa

Transactions (3)

Coinbase48adc04fec5bd3…8d54fbe198e3ff

1 in → 1 out10.1800 XPM109 B

Ad786hwV…M41PPm9x

45335e1235c7ef…cdcbfd2b669ab2

8 in → 2 out11.0160 XPM1.20 KB

AFz9fXym…wh4UqpkL AWD7v3LL…fc6WTzXf

35e6865011dd4b…16b8d7ddc0e567

1 in → 2 out6.0376 XPM226 B

AHx6Kdmd…NWEqeZ6X ANia7wgK…VR264iFL

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.

1.989 × 10⁹⁰(91-digit number)

19894123501975048184…62594144607684579279

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

1.989 × 10⁹⁰(91-digit number)

19894123501975048184…62594144607684579279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.989 × 10⁹⁰(91-digit number)

19894123501975048184…62594144607684579281

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

3.978 × 10⁹⁰(91-digit number)

39788247003950096368…25188289215369158559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.978 × 10⁹⁰(91-digit number)

39788247003950096368…25188289215369158561

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

7.957 × 10⁹⁰(91-digit number)

79576494007900192736…50376578430738317119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.957 × 10⁹⁰(91-digit number)

79576494007900192736…50376578430738317121

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

1.591 × 10⁹¹(92-digit number)

15915298801580038547…00753156861476634239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.591 × 10⁹¹(92-digit number)

15915298801580038547…00753156861476634241

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

3.183 × 10⁹¹(92-digit number)

31830597603160077094…01506313722953268479

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