Block #69,802

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 10:32:34 AM · Difficulty 8.9914 · 6,738,239 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

522d05e0f3fe3fd14ad3181c656505720c5e07e510d30e0a793e180e29fed35d

View on Chainz ↗

Height

#69,802

Difficulty

8.991395

Transactions

Size

972 B

Version

Bits

08fdcc12

Nonce

822

Timestamp

7/20/2013, 10:32:34 AM

Confirmations

6,738,239

Mined by

⛏️ P2SHASUvBvCmwS52fuGHgHup67SFs6YXYrMmir

Merkle Root

fbdc092c89cd9fdf27e657055eaefeeb20c1439d355489bbfbe208a2c94f4925

Transactions (4)

Coinbase39312f95910dd0…68f6b023e026b5

1 in → 1 out12.3800 XPM110 B

ASUvBvCm…YXYrMmir

995f39a42ff471…894599225ec2db

2 in → 1 out24.7800 XPM272 B

AaTaKq6N…LUemjxyC

ebbdc99c1cd772…7a4fd507bc0300

2 in → 1 out100.0000 XPM340 B

AW7aqm7z…MZ7TogRx

fe927e56e1e994…266e5258626eae

1 in → 1 out12.3600 XPM158 B

AREJRekG…a8dWbE8j

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.

7.594 × 10⁹⁹(100-digit number)

75945912201006052602…10503647848130420269

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

7.594 × 10⁹⁹(100-digit number)

75945912201006052602…10503647848130420269

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.594 × 10⁹⁹(100-digit number)

75945912201006052602…10503647848130420271

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

1.518 × 10¹⁰⁰(101-digit number)

15189182440201210520…21007295696260840539

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.518 × 10¹⁰⁰(101-digit number)

15189182440201210520…21007295696260840541

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

3.037 × 10¹⁰⁰(101-digit number)

30378364880402421040…42014591392521681079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.037 × 10¹⁰⁰(101-digit number)

30378364880402421040…42014591392521681081

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

6.075 × 10¹⁰⁰(101-digit number)

60756729760804842081…84029182785043362159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.075 × 10¹⁰⁰(101-digit number)

60756729760804842081…84029182785043362161

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

1.215 × 10¹⁰¹(102-digit number)

12151345952160968416…68058365570086724319

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 #69,802

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