Block #131,885

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/24/2013, 2:12:56 PM · Difficulty 9.7860 · 6,661,138 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2bc4e70917c8e175fe8c856417808c8435a37dccf66d32165eaa5a3d122dd5e2

View on Chainz ↗

Height

#131,885

Difficulty

9.785974

Transactions

Size

2.97 KB

Version

Bits

09c9359c

Nonce

249,454

Timestamp

8/24/2013, 2:12:56 PM

Confirmations

6,661,138

Merkle Root

62625401cd35d70adeeaf39bd7924a343ffc014a9fdf2c02ee1bd75ade47dae5

Transactions (3)

Coinbase9798db46938843…241a07fff70723

1 in → 1 out10.4700 XPM109 B

ALRujQRD…k6ivJZNp

4605207db5eb22…69b1eccc60d093

16 in → 1 out255.6416 XPM2.12 KB

AWjfNchA…3r8YxoQa

a53495f17cac1b…26191c2251898a

4 in → 2 out1.0106 XPM671 B

AH2Fexct…xk24sRXd AFyR2R3n…tR5c7TTz

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.

5.806 × 10⁹⁴(95-digit number)

58065165858189124584…04511698669221511899

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

5.806 × 10⁹⁴(95-digit number)

58065165858189124584…04511698669221511899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.806 × 10⁹⁴(95-digit number)

58065165858189124584…04511698669221511901

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

1.161 × 10⁹⁵(96-digit number)

11613033171637824916…09023397338443023799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.161 × 10⁹⁵(96-digit number)

11613033171637824916…09023397338443023801

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

2.322 × 10⁹⁵(96-digit number)

23226066343275649833…18046794676886047599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.322 × 10⁹⁵(96-digit number)

23226066343275649833…18046794676886047601

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

4.645 × 10⁹⁵(96-digit number)

46452132686551299667…36093589353772095199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.645 × 10⁹⁵(96-digit number)

46452132686551299667…36093589353772095201

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

9.290 × 10⁹⁵(96-digit number)

92904265373102599334…72187178707544190399

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