Block #206,044

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/12/2013, 1:20:09 PM · Difficulty 9.9006 · 6,603,408 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c63539c393df6c30e7ffc33a1eaa473b6e0ba99984ff3bfd79c5c73ccd4c0a8d

View on Chainz ↗

Height

#206,044

Difficulty

9.900648

Transactions

Size

6.94 KB

Version

Bits

09e690e5

Nonce

25,575

Timestamp

10/12/2013, 1:20:09 PM

Confirmations

6,603,408

Mined by

⛏️ P2SHAUoWr5tYE7yALVAdbB6VfPZzAPMWSEj9zP

Merkle Root

30d83541b371ad74ac78c39b639986fef6c857470693a377c0605c753a8c4992

Transactions (3)

Coinbasecc91902182fae0…7a7c0808cf1c10

1 in → 1 out10.2700 XPM109 B

AUoWr5tY…MWSEj9zP

19745f35e159a4…3d892ddd9c1cf1

57 in → 2 out552.0114 XPM6.53 KB

AQAvQSWZ…C9mFkvux AX73dxCy…fMsyAg1C

30acf75bf4d3d9…0a16d18d3cf3ba

1 in → 2 out10.1900 XPM227 B

AKv4Rt26…4Y1TKhfq ANShBaCx…NttHiwPk

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.

1.370 × 10⁹²(93-digit number)

13708029366515965020…76298819489637587199

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

1.370 × 10⁹²(93-digit number)

13708029366515965020…76298819489637587199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.370 × 10⁹²(93-digit number)

13708029366515965020…76298819489637587201

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

2.741 × 10⁹²(93-digit number)

27416058733031930041…52597638979275174399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.741 × 10⁹²(93-digit number)

27416058733031930041…52597638979275174401

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

5.483 × 10⁹²(93-digit number)

54832117466063860083…05195277958550348799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.483 × 10⁹²(93-digit number)

54832117466063860083…05195277958550348801

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

1.096 × 10⁹³(94-digit number)

10966423493212772016…10390555917100697599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.096 × 10⁹³(94-digit number)

10966423493212772016…10390555917100697601

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

2.193 × 10⁹³(94-digit number)

21932846986425544033…20781111834201395199

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 #206,044

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