Block #151,338

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/5/2013, 3:06:56 PM · Difficulty 9.8602 · 6,638,650 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

698070e3b9aaee6b0bbbe79485c895e31ee25525cde92fc99981764a5093aec7

View on Chainz ↗

Height

#151,338

Difficulty

9.860178

Transactions

Size

1.08 KB

Version

Bits

09dc34a6

Nonce

113,948

Timestamp

9/5/2013, 3:06:56 PM

Confirmations

6,638,650

Merkle Root

f4f1b29ade61b8f75150380f1ed1acf21bec5ea6a214ac457084676958531e10

Transactions (5)

Coinbase53a40c975b2563…d62ac04257e583

1 in → 1 out10.3100 XPM109 B

AWsEijaA…9WbDL6tH

dadea9432f1d4e…739bdfef97a26f

1 in → 2 out10.2700 XPM226 B

AS6LaGt9…ZZgLwduP AMbuNJN7…YDE5NsBF

a23b3500c2f4ca…3ec626fd9016e5

1 in → 2 out10.2700 XPM226 B

AJsZLCp2…7c9dqZAe AaamjEDB…UqchbkWj

9b5c941b594cb3…dbc9b8a8c7dcb3

1 in → 2 out10.2700 XPM227 B

AcN7Mwej…Rnr1man2 AMsF2Mw6…insGjf7K

81ffb59cccf3cb…18fadfc496cd79

1 in → 2 out2.9357 XPM226 B

ALz3uSwR…DHKjj4EL ARSGUtir…4X39uWEs

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.

1.172 × 10⁹³(94-digit number)

11729882562009652283…47397735235534841279

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

1.172 × 10⁹³(94-digit number)

11729882562009652283…47397735235534841279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.172 × 10⁹³(94-digit number)

11729882562009652283…47397735235534841281

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

2.345 × 10⁹³(94-digit number)

23459765124019304567…94795470471069682559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.345 × 10⁹³(94-digit number)

23459765124019304567…94795470471069682561

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

4.691 × 10⁹³(94-digit number)

46919530248038609135…89590940942139365119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.691 × 10⁹³(94-digit number)

46919530248038609135…89590940942139365121

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

9.383 × 10⁹³(94-digit number)

93839060496077218270…79181881884278730239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.383 × 10⁹³(94-digit number)

93839060496077218270…79181881884278730241

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

1.876 × 10⁹⁴(95-digit number)

18767812099215443654…58363763768557460479

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