Block #208,279

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/13/2013, 10:24:29 PM · Difficulty 9.9056 · 6,585,989 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

621c6705e09177a0927f600b2d340d81fce86e371c4d7d21742d4f7f592d5fa5

View on Chainz ↗

Height

#208,279

Difficulty

9.905566

Transactions

Size

844 B

Version

Bits

09e7d332

Nonce

44,482

Timestamp

10/13/2013, 10:24:29 PM

Confirmations

6,585,989

Merkle Root

71049e038c41730163b3e60881d9949287e24b568da7a9729d68633b8f542f3c

Transactions (4)

Coinbasebec0a153351a3b…76092c16c5a7ef

1 in → 1 out10.2108 XPM109 B

AXQH9wDW…x7ntygiW

1fbde18e1afa86…c186c9d911aa4f

1 in → 1 out5.0730 XPM192 B

AVbUYygu…86BSkU3f

2507bed1eecfcc…ecf7d862a4c800

1 in → 2 out2.5353 XPM226 B

AbNXXQ3F…e7jXejV9 AGpaVNHd…HcRsU2CA

dbd4866d07c55a…581d53a1dd0255

1 in → 2 out3.1879 XPM226 B

ATvdc8Fq…z4MS5pim AMJDChGB…VXxUjXFK

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.

9.374 × 10⁹⁵(96-digit number)

93742592065511170127…07954475618304753899

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

9.374 × 10⁹⁵(96-digit number)

93742592065511170127…07954475618304753899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.374 × 10⁹⁵(96-digit number)

93742592065511170127…07954475618304753901

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

1.874 × 10⁹⁶(97-digit number)

18748518413102234025…15908951236609507799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.874 × 10⁹⁶(97-digit number)

18748518413102234025…15908951236609507801

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

3.749 × 10⁹⁶(97-digit number)

37497036826204468050…31817902473219015599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.749 × 10⁹⁶(97-digit number)

37497036826204468050…31817902473219015601

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

7.499 × 10⁹⁶(97-digit number)

74994073652408936101…63635804946438031199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.499 × 10⁹⁶(97-digit number)

74994073652408936101…63635804946438031201

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

1.499 × 10⁹⁷(98-digit number)

14998814730481787220…27271609892876062399

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