Block #175,070

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/22/2013, 1:31:12 AM · Difficulty 9.8633 · 6,631,445 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

836a27896db4708bf0c53fff91d145e06cf880ea1f70fc74cacf671778aa3d50

View on Chainz ↗

Height

#175,070

Difficulty

9.863271

Transactions

Size

1.41 KB

Version

Bits

09dcff53

Nonce

132,647

Timestamp

9/22/2013, 1:31:12 AM

Confirmations

6,631,445

Mined by

⛏️ P2SHAU6QKW8rDqYwcBRfNXXiLBJPXnVJw6HhTn

Merkle Root

aa287df12a48bb8feb61847cf6534f53dcb85b71fc68a427b277b52c407f3a6c

Transactions (5)

Coinbasee22ddb82149a75…efd265dcc1de0c

1 in → 1 out10.3000 XPM109 B

AU6QKW8r…VJw6HhTn

49e06c3015a134…227e770496b89c

4 in → 1 out41.2500 XPM567 B

AWMpmDAz…tXnUHg2J

1fd828890ce1de…175f50f4122f80

1 in → 2 out10.2500 XPM225 B

Abx5qH6G…Hh56BvNt AYPX18BZ…hMRZit3W

ba7ac6e30e1e7d…cd135514b155f0

1 in → 2 out10.2500 XPM225 B

APXuvjkg…PXtRYGMK AK8thoR2…gfNRR8XN

f528bf25ac71d6…96b88d93432627

1 in → 2 out3.1418 XPM226 B

APy2MDf3…WUdjpDGP AZfh2ZBY…61cvCq8F

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.

3.141 × 10¹⁰⁵(106-digit number)

31415813142335801536…01142711223146961079

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

3.141 × 10¹⁰⁵(106-digit number)

31415813142335801536…01142711223146961079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.141 × 10¹⁰⁵(106-digit number)

31415813142335801536…01142711223146961081

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

6.283 × 10¹⁰⁵(106-digit number)

62831626284671603072…02285422446293922159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.283 × 10¹⁰⁵(106-digit number)

62831626284671603072…02285422446293922161

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

1.256 × 10¹⁰⁶(107-digit number)

12566325256934320614…04570844892587844319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.256 × 10¹⁰⁶(107-digit number)

12566325256934320614…04570844892587844321

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

2.513 × 10¹⁰⁶(107-digit number)

25132650513868641228…09141689785175688639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.513 × 10¹⁰⁶(107-digit number)

25132650513868641228…09141689785175688641

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

5.026 × 10¹⁰⁶(107-digit number)

50265301027737282457…18283379570351377279

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 #175,070

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