Block #212,137

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/16/2013, 2:48:15 AM · Difficulty 9.9182 · 6,582,665 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3da4529ceeb70e02e98a5cc028c0c3d16182c2e4c459903a9bcbd021226a5029

View on Chainz ↗

Height

#212,137

Difficulty

9.918241

Transactions

Size

2.49 KB

Version

Bits

09eb11d8

Nonce

48,739

Timestamp

10/16/2013, 2:48:15 AM

Confirmations

6,582,665

Mined by

⛏️ P2SHARj8Ze2dVHC93XTVihrs6HdQKgYJCdkQE2

Merkle Root

a899d5ba0e7b8e4126d60374024e20cecf0e0ba0030565b170328ac3f82ecf4f

Transactions (5)

Coinbase1a7b9bf039f754…d36171ed783382

1 in → 1 out10.2000 XPM109 B

ARj8Ze2d…YJCdkQE2

230153416ce2ef…7df42324487ae3

4 in → 2 out749.9070 XPM668 B

AeRJFyNH…g8j2mngP Ac7RAQMV…nKWU2GLU

005fcbc2dcf5a9…a04871e50c41d0

3 in → 1 out897.9900 XPM490 B

AKQqJp7Q…dgNJtX5a

64eeb989295fd4…59968ca185d7eb

2 in → 2 out10.7752 XPM373 B

AXnPFR4U…kcLh1H5t ASuoUi24…FwBoFbxd

6080366f3c0cc9…580169f9d52338

5 in → 2 out5.0155 XPM819 B

AbjvVS5v…6ghEBPF1 AH3dDrPX…iXBYe8ZV

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.

1.190 × 10⁹⁵(96-digit number)

11909024448308505082…60362413820309748189

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

1.190 × 10⁹⁵(96-digit number)

11909024448308505082…60362413820309748189

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.190 × 10⁹⁵(96-digit number)

11909024448308505082…60362413820309748191

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

2.381 × 10⁹⁵(96-digit number)

23818048896617010164…20724827640619496379

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.381 × 10⁹⁵(96-digit number)

23818048896617010164…20724827640619496381

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

4.763 × 10⁹⁵(96-digit number)

47636097793234020328…41449655281238992759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.763 × 10⁹⁵(96-digit number)

47636097793234020328…41449655281238992761

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

9.527 × 10⁹⁵(96-digit number)

95272195586468040657…82899310562477985519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.527 × 10⁹⁵(96-digit number)

95272195586468040657…82899310562477985521

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

1.905 × 10⁹⁶(97-digit number)

19054439117293608131…65798621124955971039

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