Block #171,317

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/19/2013, 10:04:18 AM · Difficulty 9.8644 · 6,623,743 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b0ec4743ae962a392e6bbdf9fb8044f52a906f49b23fe114ae306654ed153137

View on Chainz ↗

Height

#171,317

Difficulty

9.864379

Transactions

Size

1.60 KB

Version

Bits

09dd47f9

Nonce

14,929

Timestamp

9/19/2013, 10:04:18 AM

Confirmations

6,623,743

Mined by

⛏️ P2SHAePL1u7nVnZ9poRVpD9AcAa3CSN6KebdPp

Merkle Root

0e866b612278aac74ab1ddfdb91b8ed54faede86b550f24cc1dd759bbb8a52fe

Transactions (3)

Coinbase69506bc17f8946…4622a69ea2ae87

1 in → 1 out10.2900 XPM109 B

AePL1u7n…N6KebdPp

2cad10f5be5e5d…e3a3cfc921a4a8

7 in → 6 out16.1767 XPM1.19 KB

AU5g73DE…hY8WccpK AcyPVp7N…dDULWcdA ARtPXKuc…KzX35CG6 AVYebXcy…Hb6vMiyi Af5j3R6a…XH9ngznA

32212fca203bdd…e59d1854033871

1 in → 2 out7.7177 XPM226 B

AJAy7JZp…gk8XwtMv AXwKKGcU…yK2w3TwR

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.

2.511 × 10⁹⁴(95-digit number)

25112627066539740479…92153046958757912749

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

2.511 × 10⁹⁴(95-digit number)

25112627066539740479…92153046958757912749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.511 × 10⁹⁴(95-digit number)

25112627066539740479…92153046958757912751

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

5.022 × 10⁹⁴(95-digit number)

50225254133079480959…84306093917515825499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.022 × 10⁹⁴(95-digit number)

50225254133079480959…84306093917515825501

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

1.004 × 10⁹⁵(96-digit number)

10045050826615896191…68612187835031650999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.004 × 10⁹⁵(96-digit number)

10045050826615896191…68612187835031651001

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

2.009 × 10⁹⁵(96-digit number)

20090101653231792383…37224375670063301999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.009 × 10⁹⁵(96-digit number)

20090101653231792383…37224375670063302001

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

4.018 × 10⁹⁵(96-digit number)

40180203306463584767…74448751340126603999

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