Block #176,731

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/23/2013, 4:00:49 AM · Difficulty 9.8652 · 6,616,292 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b71b9885414fa070850065d08031feef381ec5c1ee1d33596f81ba269447935d

View on Chainz ↗

Height

#176,731

Difficulty

9.865216

Transactions

Size

356 B

Version

Bits

09dd7ec5

Nonce

200,229

Timestamp

9/23/2013, 4:00:49 AM

Confirmations

6,616,292

Merkle Root

59158303d77a9ad02f61933ee5418626202f3bd0b4ec969b6ff5d0011cf848a3

Transactions (2)

Coinbasedc8c4e681978fe…38e6560d264e5d

1 in → 1 out10.2700 XPM109 B

AM5vAB97…XCy8Z1fg

d5b65c98227eee…c54d3c8c040d8d

1 in → 1 out10.2600 XPM157 B

Ae2P8tRG…ZBcRXaeZ

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.

1.725 × 10⁹⁵(96-digit number)

17251039861508711849…12254769047524303359

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

1.725 × 10⁹⁵(96-digit number)

17251039861508711849…12254769047524303359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.725 × 10⁹⁵(96-digit number)

17251039861508711849…12254769047524303361

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

3.450 × 10⁹⁵(96-digit number)

34502079723017423699…24509538095048606719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.450 × 10⁹⁵(96-digit number)

34502079723017423699…24509538095048606721

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

6.900 × 10⁹⁵(96-digit number)

69004159446034847398…49019076190097213439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.900 × 10⁹⁵(96-digit number)

69004159446034847398…49019076190097213441

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

1.380 × 10⁹⁶(97-digit number)

13800831889206969479…98038152380194426879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.380 × 10⁹⁶(97-digit number)

13800831889206969479…98038152380194426881

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

2.760 × 10⁹⁶(97-digit number)

27601663778413938959…96076304760388853759

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