Block #214,889

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/17/2013, 6:17:02 PM · Difficulty 9.9244 · 6,593,081 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bccff4b0e47f7727b7684b3d32e01f82d28f78b42fa4e505889a1ea5c73d4452

View on Chainz ↗

Height

#214,889

Difficulty

9.924367

Transactions

Size

4.93 KB

Version

Bits

09eca351

Nonce

1,164,968,514

Timestamp

10/17/2013, 6:17:02 PM

Confirmations

6,593,081

Mined by

⛏️ iGR`AbdqpFgmN6ooQ1qcRqkeX1J4AKM8UVG4YE

Merkle Root

d35e725f230aeaa2d142889bd4ec27d2fa8f45c9024721a4857b5e86f383e396

Transactions (1)

Coinbased35e725f230aea…7b5e86f383e396

1 in → 144 out10.0900 XPM4.84 KB

AbdqpFgm…M8UVG4YE AdqZDct3…Y1D432wN APZoG4ZW…MqYepZby ASBFyn8Q…gDcPEt7u AMFZUpsP…4akTRV6E

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.

1.815 × 10⁹³(94-digit number)

18158107652872795025…86145053612723500179

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

1.815 × 10⁹³(94-digit number)

18158107652872795025…86145053612723500179

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.815 × 10⁹³(94-digit number)

18158107652872795025…86145053612723500181

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

3.631 × 10⁹³(94-digit number)

36316215305745590050…72290107225447000359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.631 × 10⁹³(94-digit number)

36316215305745590050…72290107225447000361

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

7.263 × 10⁹³(94-digit number)

72632430611491180100…44580214450894000719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.263 × 10⁹³(94-digit number)

72632430611491180100…44580214450894000721

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

1.452 × 10⁹⁴(95-digit number)

14526486122298236020…89160428901788001439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.452 × 10⁹⁴(95-digit number)

14526486122298236020…89160428901788001441

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

2.905 × 10⁹⁴(95-digit number)

29052972244596472040…78320857803576002879

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 #214,889

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