Block #595,130

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/20/2014, 2:06:34 AM · Difficulty 10.9372 · 6,222,713 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dedca691ae1f393d894aab52077ec06065ab13f64b848ccaaa8ce64fcae9e6ea

View on Chainz ↗

Height

#595,130

Difficulty

10.937169

Transactions

Size

886 B

Version

Bits

0aefea4c

Nonce

1,243,320,325

Timestamp

6/20/2014, 2:06:34 AM

Confirmations

6,222,713

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

85dce3863072b673eb616a0135819f59a9cac38f408524086f0e62b4e3629e1c

Transactions (4)

Coinbase320d10e77fa206…911c6a734ca75b

1 in → 1 out8.3800 XPM116 B

ANSXnLY2…Sd25TjkD

e3e61e1135cbdc…1c702867d87d52

1 in → 2 out6.2834 XPM226 B

AYLyEVs6…bBQP1JVN AGdWVjRk…LFVsqCnK

9f91ae49d7055f…c4637e36a0eb2c

1 in → 2 out2.5209 XPM225 B

AToctXWm…mgEtBv9N AcRwZMXe…L173Q4Wf

d11e70af671c04…b6047d0ba63442

1 in → 2 out5.8431 XPM227 B

ARjW1anf…MdvEKg9s ANjjWJLU…Vpb1jjKT

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.

1.403 × 10⁹⁹(100-digit number)

14037752407305846870…21336832868287511039

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

1.403 × 10⁹⁹(100-digit number)

14037752407305846870…21336832868287511039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.403 × 10⁹⁹(100-digit number)

14037752407305846870…21336832868287511041

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

2.807 × 10⁹⁹(100-digit number)

28075504814611693741…42673665736575022079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.807 × 10⁹⁹(100-digit number)

28075504814611693741…42673665736575022081

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

5.615 × 10⁹⁹(100-digit number)

56151009629223387482…85347331473150044159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.615 × 10⁹⁹(100-digit number)

56151009629223387482…85347331473150044161

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

1.123 × 10¹⁰⁰(101-digit number)

11230201925844677496…70694662946300088319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.123 × 10¹⁰⁰(101-digit number)

11230201925844677496…70694662946300088321

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

2.246 × 10¹⁰⁰(101-digit number)

22460403851689354992…41389325892600176639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.246 × 10¹⁰⁰(101-digit number)

22460403851689354992…41389325892600176641

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.492 × 10¹⁰⁰(101-digit number)

44920807703378709985…82778651785200353279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #595,130

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