Block #188,161

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/1/2013, 12:28:56 AM · Difficulty 9.8698 · 6,622,043 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bfd64b1130d623349503f723e8e37d6321acbcf74b271c14b2f7e33d591c2cf7

View on Chainz ↗

Height

#188,161

Difficulty

9.869782

Transactions

Size

1.80 KB

Version

Bits

09deaa03

Nonce

32,312

Timestamp

10/1/2013, 12:28:56 AM

Confirmations

6,622,043

Mined by

⛏️ P2SHAKhAUNb9squtDf8ePc93XmtLCRLAQDUxrt

Merkle Root

2af8f2ec584feecb0121b73387c848c95e5510832919383eea9bd97cc7793095

Transactions (5)

Coinbase9dea23a123e0db…25b5dc54233790

1 in → 1 out10.2900 XPM109 B

AKhAUNb9…LAQDUxrt

c31893b0c1d24f…5a73bb382f7ab4

2 in → 2 out4.0341 XPM373 B

AQ3h66h4…cUFThtQg AZnTudst…5MHS6nom

14267ab01788c1…8f2207e4d9ded6

5 in → 2 out4.9203 XPM816 B

AWyu9emz…xXcq3D2y AR9LUS5x…XF57MupG

ec3824cb04d9a7…8958d4268ca489

1 in → 2 out40.9900 XPM226 B

AX4xVTzS…KpELCNZx AUxyyejF…tpRGQQzR

60b51f0457b336…d5f7bdb8ba3c19

1 in → 2 out3.0996 XPM227 B

AKAE2W1C…2yHyVVmT AURSPfon…u77GsQUC

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.

1.607 × 10⁹⁵(96-digit number)

16078578174084944542…44791144614446037279

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

1.607 × 10⁹⁵(96-digit number)

16078578174084944542…44791144614446037279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.607 × 10⁹⁵(96-digit number)

16078578174084944542…44791144614446037281

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

3.215 × 10⁹⁵(96-digit number)

32157156348169889084…89582289228892074559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.215 × 10⁹⁵(96-digit number)

32157156348169889084…89582289228892074561

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

6.431 × 10⁹⁵(96-digit number)

64314312696339778169…79164578457784149119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.431 × 10⁹⁵(96-digit number)

64314312696339778169…79164578457784149121

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

1.286 × 10⁹⁶(97-digit number)

12862862539267955633…58329156915568298239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.286 × 10⁹⁶(97-digit number)

12862862539267955633…58329156915568298241

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

2.572 × 10⁹⁶(97-digit number)

25725725078535911267…16658313831136596479

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 #188,161

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