Block #119,432

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/16/2013, 11:47:02 AM · Difficulty 9.7494 · 6,687,114 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

564b88bb446782476ccf7430ee27cec5012a420cad7ea1398f3d9362c0592599

View on Chainz ↗

Height

#119,432

Difficulty

9.749376

Transactions

Size

4.32 KB

Version

Bits

09bfd713

Nonce

930,203

Timestamp

8/16/2013, 11:47:02 AM

Confirmations

6,687,114

Mined by

⛏️ P2SHAdgupwqNsJ3Dx7m31P3ZgaKirPKceX9b1w

Merkle Root

14df0920492798eb4a72db319b5ec7a6803a936f34e991b0fd72049eb395f0b7

Transactions (2)

Coinbase51dfbc35ba64fb…99da8aba36e9d9

1 in → 1 out10.5700 XPM109 B

AdgupwqN…KceX9b1w

2d35ffd19268d0…5e42a80fbccbba

28 in → 2 out5000.0106 XPM4.12 KB

AHgRf5J7…1WkCXvZh AUo5MxCt…sXvy7Uk2

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.

5.088 × 10¹⁰⁹(110-digit number)

50881162802582461984…59139191971377263379

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

5.088 × 10¹⁰⁹(110-digit number)

50881162802582461984…59139191971377263379

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.088 × 10¹⁰⁹(110-digit number)

50881162802582461984…59139191971377263381

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

1.017 × 10¹¹⁰(111-digit number)

10176232560516492396…18278383942754526759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.017 × 10¹¹⁰(111-digit number)

10176232560516492396…18278383942754526761

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

2.035 × 10¹¹⁰(111-digit number)

20352465121032984793…36556767885509053519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.035 × 10¹¹⁰(111-digit number)

20352465121032984793…36556767885509053521

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

4.070 × 10¹¹⁰(111-digit number)

40704930242065969587…73113535771018107039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.070 × 10¹¹⁰(111-digit number)

40704930242065969587…73113535771018107041

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

8.140 × 10¹¹⁰(111-digit number)

81409860484131939174…46227071542036214079

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 #119,432

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