Block #188,471

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/1/2013, 5:06:42 AM · Difficulty 9.8707 · 6,606,046 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7f20a4024a00e20c55171c7965248b4c7e3eea1aea72c83c49553b339c9ed48a

View on Chainz ↗

Height

#188,471

Difficulty

9.870665

Transactions

Size

2.58 KB

Version

Bits

09dee3e0

Nonce

37,119

Timestamp

10/1/2013, 5:06:42 AM

Confirmations

6,606,046

Mined by

⛏️ P2SHAKgCoh7CJFSvHNNuuLiHvAow1gLYsNGjDy

Merkle Root

575cb0b2c1422afb9b5afad06dbecafa5701122e639175536eb264dabb6d8293

Transactions (4)

Coinbase4a9c0070896264…deb3abf02967b5

1 in → 1 out10.2800 XPM109 B

AKgCoh7C…LYsNGjDy

eb32f1f4545a5a…f1a3095ae2d911

8 in → 1 out82.2500 XPM960 B

AMm2NR1w…19uBFzE6

9ec2b59c5d81b6…137eac0474ee97

5 in → 2 out51.3400 XPM816 B

AZ6quks9…rarZiN6o ANP3mT5K…dkjrtVpK

cba5e9a89e51e1…8e92eb8f50f77f

4 in → 2 out30.6515 XPM670 B

AVRW3C4A…kRS9xvZa AZoTowvW…KJoS4PJA

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.

2.638 × 10⁹⁹(100-digit number)

26387243603494646273…82445568663123724359

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

2.638 × 10⁹⁹(100-digit number)

26387243603494646273…82445568663123724359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.638 × 10⁹⁹(100-digit number)

26387243603494646273…82445568663123724361

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

5.277 × 10⁹⁹(100-digit number)

52774487206989292546…64891137326247448719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.277 × 10⁹⁹(100-digit number)

52774487206989292546…64891137326247448721

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

1.055 × 10¹⁰⁰(101-digit number)

10554897441397858509…29782274652494897439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.055 × 10¹⁰⁰(101-digit number)

10554897441397858509…29782274652494897441

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

2.110 × 10¹⁰⁰(101-digit number)

21109794882795717018…59564549304989794879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.110 × 10¹⁰⁰(101-digit number)

21109794882795717018…59564549304989794881

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

4.221 × 10¹⁰⁰(101-digit number)

42219589765591434036…19129098609979589759

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