Block #129,546

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/23/2013, 12:11:42 AM · Difficulty 9.7835 · 6,684,316 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

545fbbd57a354653a8b754155d4da74c9590e6af98ae02e02aabd1b6f5f78ef6

View on Chainz ↗

Height

#129,546

Difficulty

9.783487

Transactions

Size

393 B

Version

Bits

09c89299

Nonce

212,672

Timestamp

8/23/2013, 12:11:42 AM

Confirmations

6,684,316

Mined by

⛏️ P2SHASki8pmAYiSmpQcpe6L3Yu14B9Dwetzr7b

Merkle Root

bf791a90f32de4f6a51bfb2c1094ce5f894d6af783a6cdfc05e693cc9afcb94c

Transactions (2)

Coinbase28a70f2b343e0e…f9a6b38eb2f3b7

1 in → 1 out10.4400 XPM109 B

ASki8pmA…Dwetzr7b

2223cde738e85d…fae7273d730e8c

1 in → 2 out10.4400 XPM192 B

AGZvBxxa…shhkwtTn AcSsGz85…Cky1jhYQ

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.

8.855 × 10⁹⁹(100-digit number)

88554020471303191247…04118249910373965589

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

8.855 × 10⁹⁹(100-digit number)

88554020471303191247…04118249910373965589

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.855 × 10⁹⁹(100-digit number)

88554020471303191247…04118249910373965591

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

1.771 × 10¹⁰⁰(101-digit number)

17710804094260638249…08236499820747931179

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.771 × 10¹⁰⁰(101-digit number)

17710804094260638249…08236499820747931181

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

3.542 × 10¹⁰⁰(101-digit number)

35421608188521276499…16472999641495862359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.542 × 10¹⁰⁰(101-digit number)

35421608188521276499…16472999641495862361

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

7.084 × 10¹⁰⁰(101-digit number)

70843216377042552998…32945999282991724719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.084 × 10¹⁰⁰(101-digit number)

70843216377042552998…32945999282991724721

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

1.416 × 10¹⁰¹(102-digit number)

14168643275408510599…65891998565983449439

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 #129,546

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