Block #265,932

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/20/2013, 12:48:36 AM · Difficulty 9.9614 · 6,537,615 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6bf9f7b7a0f298f8893665f1190bb28efc3971e10c2c792888567bd831fc9e34

View on Chainz ↗

Height

#265,932

Difficulty

9.961351

Transactions

Size

1.33 KB

Version

Bits

09f61b13

Nonce

37,739

Timestamp

11/20/2013, 12:48:36 AM

Confirmations

6,537,615

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

e9746d6c5f79496276d279c3af85eb5c3511d8e0f8fd1dc55b196d3bcad6fa7e

Transactions (4)

Coinbaseefaf624a3a7612…b486c1c0cd69de

1 in → 2 out10.0900 XPM141 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

0d80980326ebc4…d545aad3ae2189

1 in → 2 out10.0200 XPM226 B

AHJFoooV…sAYN5LL4 AGsoNQ8k…jc6fx4Tk

aae20fe7bac529…4f6a30e4f0cfb4

1 in → 2 out5.8573 XPM227 B

AJtQEqUL…cLE2Gkfm ALFc8LRZ…ScHJkkuG

6ebc9b6c355394…040071b89a00c7

4 in → 2 out2.1211 XPM669 B

ANL6t3We…VhSot2V9 Aab5RKGd…Exjw7EZz

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.

2.482 × 10¹⁰³(104-digit number)

24821707723285541052…49996045389783040879

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

2.482 × 10¹⁰³(104-digit number)

24821707723285541052…49996045389783040879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.482 × 10¹⁰³(104-digit number)

24821707723285541052…49996045389783040881

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

4.964 × 10¹⁰³(104-digit number)

49643415446571082105…99992090779566081759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.964 × 10¹⁰³(104-digit number)

49643415446571082105…99992090779566081761

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

9.928 × 10¹⁰³(104-digit number)

99286830893142164211…99984181559132163519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.928 × 10¹⁰³(104-digit number)

99286830893142164211…99984181559132163521

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

1.985 × 10¹⁰⁴(105-digit number)

19857366178628432842…99968363118264327039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.985 × 10¹⁰⁴(105-digit number)

19857366178628432842…99968363118264327041

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

3.971 × 10¹⁰⁴(105-digit number)

39714732357256865684…99936726236528654079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.971 × 10¹⁰⁴(105-digit number)

39714732357256865684…99936726236528654081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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