Block #208,273

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/13/2013, 10:19:25 PM · Difficulty 9.9055 · 6,602,719 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

10f61649385c461f3cfb49b3690942f041d9192845004a94a13dcc162c97e22a

View on Chainz ↗

Height

#208,273

Difficulty

9.905548

Transactions

Size

1.34 KB

Version

Bits

09e7d204

Nonce

8,889

Timestamp

10/13/2013, 10:19:25 PM

Confirmations

6,602,719

Mined by

⛏️ P2SHAVQtj9szcPSbXf2Kn31DQ2okAd4P34aCDq

Merkle Root

0f7063ef7f73b991365dba516c1a69e5a76995c6454e42fdc811020374916f3e

Transactions (4)

Coinbase8159a734a5473d…594a65926a1c6e

1 in → 1 out10.2100 XPM109 B

AVQtj9sz…4P34aCDq

572a69cde7223d…eb7c113a2facff

1 in → 1 out10.2000 XPM158 B

AZQYC8x2…1JEaWFmY

7a324be94e7abb…3a8076ed3db1d2

5 in → 2 out50.9400 XPM820 B

ANXRdRuP…zMQRWm9d ANP3mT5K…dkjrtVpK

d5789bde10b311…e239377bee21ea

1 in → 1 out2.9914 XPM193 B

ASazCFjo…nA3y7k5f

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.

4.229 × 10⁹⁵(96-digit number)

42293313467357625113…06701295501072109579

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

4.229 × 10⁹⁵(96-digit number)

42293313467357625113…06701295501072109579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.229 × 10⁹⁵(96-digit number)

42293313467357625113…06701295501072109581

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

8.458 × 10⁹⁵(96-digit number)

84586626934715250226…13402591002144219159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.458 × 10⁹⁵(96-digit number)

84586626934715250226…13402591002144219161

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

1.691 × 10⁹⁶(97-digit number)

16917325386943050045…26805182004288438319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.691 × 10⁹⁶(97-digit number)

16917325386943050045…26805182004288438321

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

3.383 × 10⁹⁶(97-digit number)

33834650773886100090…53610364008576876639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.383 × 10⁹⁶(97-digit number)

33834650773886100090…53610364008576876641

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

6.766 × 10⁹⁶(97-digit number)

67669301547772200181…07220728017153753279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.766 × 10⁹⁶(97-digit number)

67669301547772200181…07220728017153753281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #208,273

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