Block #236,629

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 2:26:44 PM · Difficulty 9.9481 · 6,588,263 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a8d63ee47b5959a8e29ac0abecbaac0ce64bd12d4f184ced08333e4a6a12562a

View on Chainz ↗

Height

#236,629

Difficulty

9.948071

Transactions

Size

2.09 KB

Version

Bits

09f2b4c0

Nonce

71,484

Timestamp

10/31/2013, 2:26:44 PM

Confirmations

6,588,263

Mined by

⛏️ P2SHASwXACnaqxmD8B7g3NyPes9iwkRU3kLr9W

Merkle Root

1773eb7f8fb8bc0153c9174b319b4534e641cae852610f7325846883a7c0e982

Transactions (5)

Coinbased86e8223b3cc48…ff028694f19390

1 in → 1 out10.1300 XPM109 B

ASwXACna…RU3kLr9W

62644084959457…bca718c53c3844

4 in → 2 out40.3900 XPM672 B

AQAvQSWZ…C9mFkvux ASySyYmp…xSuiPLKG

59a9771c0b83a7…0a2b66cc55c8fa

2 in → 2 out20.1900 XPM372 B

AbQVuXmJ…qZjmTccE AHJXEEoo…tF7t8CP8

0717b1cca225ae…1b24294691d4f7

1 in → 2 out10.0900 XPM227 B

Ac3zhp5B…YhCWdN9b AaYBJ5QB…D82bB7Rd

0ff0ccd760034e…45811bd85071d9

4 in → 2 out2.0508 XPM670 B

AWe3MGJp…orS4UKdW AGyhc9Ym…YqF23X8n

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.

2.426 × 10⁹³(94-digit number)

24267101393201559500…16536410136338631679

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

2.426 × 10⁹³(94-digit number)

24267101393201559500…16536410136338631679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.426 × 10⁹³(94-digit number)

24267101393201559500…16536410136338631681

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

4.853 × 10⁹³(94-digit number)

48534202786403119000…33072820272677263359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.853 × 10⁹³(94-digit number)

48534202786403119000…33072820272677263361

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

9.706 × 10⁹³(94-digit number)

97068405572806238000…66145640545354526719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.706 × 10⁹³(94-digit number)

97068405572806238000…66145640545354526721

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

1.941 × 10⁹⁴(95-digit number)

19413681114561247600…32291281090709053439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.941 × 10⁹⁴(95-digit number)

19413681114561247600…32291281090709053441

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

3.882 × 10⁹⁴(95-digit number)

38827362229122495200…64582562181418106879

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 #236,629

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