Block #206,706

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/12/2013, 11:44:44 PM · Difficulty 9.9014 · 6,637,176 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2d27693b4a65d812354d36547f3596e635eba31810de7bfabebfe9bc1fb72075

View on Chainz ↗

Height

#206,706

Difficulty

9.901416

Transactions

Size

197 B

Version

Bits

09e6c32c

Nonce

127,095

Timestamp

10/12/2013, 11:44:44 PM

Confirmations

6,637,176

Mined by

⛏️ P2SHAYRQNrskaTHsmMyH8DqHT4QgMSexrkctCo

Merkle Root

6d4cf1542b10bef0b50c37e152cec7889da5ed4884469bd4e57bc3389b5341db

Transactions (1)

Coinbase6d4cf1542b10be…7bc3389b5341db

1 in → 1 out10.1800 XPM109 B

AYRQNrsk…exrkctCo

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.

3.638 × 10⁹⁰(91-digit number)

36388285266918489260…37194126453118944319

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

3.638 × 10⁹⁰(91-digit number)

36388285266918489260…37194126453118944319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.638 × 10⁹⁰(91-digit number)

36388285266918489260…37194126453118944321

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

7.277 × 10⁹⁰(91-digit number)

72776570533836978521…74388252906237888639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.277 × 10⁹⁰(91-digit number)

72776570533836978521…74388252906237888641

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

1.455 × 10⁹¹(92-digit number)

14555314106767395704…48776505812475777279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.455 × 10⁹¹(92-digit number)

14555314106767395704…48776505812475777281

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

2.911 × 10⁹¹(92-digit number)

29110628213534791408…97553011624951554559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.911 × 10⁹¹(92-digit number)

29110628213534791408…97553011624951554561

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

5.822 × 10⁹¹(92-digit number)

58221256427069582817…95106023249903109119

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 #206,706

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