Block #3,493,565

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/30/2019, 2:56:53 AM · Difficulty 10.9513 · 3,315,958 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0061abb1dd5da7c1082790a2c9a217b43e1fb952c4afb50896dbc43f08ff8bee

View on Chainz ↗

Height

#3,493,565

Difficulty

10.951278

Transactions

Size

881 B

Version

Bits

0af386f5

Nonce

226,603,218

Timestamp

12/30/2019, 2:56:53 AM

Confirmations

3,315,958

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

3c1187f7b534074ee1ead35af31b31a6776b912b50efb823a6819d4f6afa66b7

Transactions (3)

Coinbasef873c51c7af755…41d804446308f7

1 in → 1 out8.3400 XPM110 B

ASiq2qtK…VMhmk7yL

11beaf6499783d…8223fd6ed82979

2 in → 2 out13.2100 XPM342 B

AGtEZEiY…AGV66d5y AcbNyGLi…AMSPTig9

69ed976bc5c1da…f74ca086d2065b

2 in → 2 out11.5100 XPM339 B

ALh3G4wq…cFPms2mF AJwfLJ8K…go1R7n2c

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.

1.869 × 10⁹⁵(96-digit number)

18699153449524651033…33812881742202042559

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

1.869 × 10⁹⁵(96-digit number)

18699153449524651033…33812881742202042559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.869 × 10⁹⁵(96-digit number)

18699153449524651033…33812881742202042561

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

3.739 × 10⁹⁵(96-digit number)

37398306899049302067…67625763484404085119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.739 × 10⁹⁵(96-digit number)

37398306899049302067…67625763484404085121

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

7.479 × 10⁹⁵(96-digit number)

74796613798098604134…35251526968808170239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.479 × 10⁹⁵(96-digit number)

74796613798098604134…35251526968808170241

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

1.495 × 10⁹⁶(97-digit number)

14959322759619720826…70503053937616340479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.495 × 10⁹⁶(97-digit number)

14959322759619720826…70503053937616340481

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

2.991 × 10⁹⁶(97-digit number)

29918645519239441653…41006107875232680959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.991 × 10⁹⁶(97-digit number)

29918645519239441653…41006107875232680961

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

5.983 × 10⁹⁶(97-digit number)

59837291038478883307…82012215750465361919

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 #3,493,565

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