Block #208,576

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/14/2013, 2:05:27 AM · Difficulty 9.9070 · 6,586,427 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dbb46bfdbc4d3304cd5990f07a974fa3c21ddec82527f5445805babf5908ad1c

View on Chainz ↗

Height

#208,576

Difficulty

9.907006

Transactions

Size

799 B

Version

Bits

09e8318c

Nonce

59,868

Timestamp

10/14/2013, 2:05:27 AM

Confirmations

6,586,427

Mined by

⛏️ P2SHAc2ybeQyrJv9dLgwx5Bs4g5b1SZdEVZHdg

Merkle Root

d1a849a82043e3b432c6e18e1fc5e65f3c6a9c5fcde7e8bb8cd002e262b7e40d

Transactions (3)

Coinbase781080eb1123c0…d89863988a7a66

1 in → 1 out10.1900 XPM109 B

Ac2ybeQy…ZdEVZHdg

b0fde7f8886217…0d9fc1ef88e4d4

2 in → 2 out20.3700 XPM373 B

AcFNUzkU…W6Gq8U8o ASuoUi24…FwBoFbxd

6dab86331fb7bd…34572a0e7747c9

1 in → 2 out10.1800 XPM227 B

AVYA5FSq…eeZm8KGY ASoQqrjk…JfE1Ku1t

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.

5.601 × 10⁹⁵(96-digit number)

56015289651910329300…77952222389203873279

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

5.601 × 10⁹⁵(96-digit number)

56015289651910329300…77952222389203873279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.601 × 10⁹⁵(96-digit number)

56015289651910329300…77952222389203873281

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

1.120 × 10⁹⁶(97-digit number)

11203057930382065860…55904444778407746559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.120 × 10⁹⁶(97-digit number)

11203057930382065860…55904444778407746561

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

2.240 × 10⁹⁶(97-digit number)

22406115860764131720…11808889556815493119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.240 × 10⁹⁶(97-digit number)

22406115860764131720…11808889556815493121

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

4.481 × 10⁹⁶(97-digit number)

44812231721528263440…23617779113630986239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.481 × 10⁹⁶(97-digit number)

44812231721528263440…23617779113630986241

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

8.962 × 10⁹⁶(97-digit number)

89624463443056526881…47235558227261972479

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