Block #53,252

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/16/2013, 2:26:50 PM · Difficulty 8.9215 · 6,738,461 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6a9db186f7e14e8eb162388e3726f491215a2644ec5bcd546b22575a8f11bd7c

View on Chainz ↗

Height

#53,252

Difficulty

8.921491

Transactions

Size

204 B

Version

Bits

08ebe6cf

Nonce

Timestamp

7/16/2013, 2:26:50 PM

Confirmations

6,738,461

Merkle Root

e2d785195ad606ad7f067225650520bfd6cac3f31b8278130495f1a8cb7db055

Transactions (1)

Coinbasee2d785195ad606…95f1a8cb7db055

1 in → 1 out12.5500 XPM109 B

AQEbmWMh…bVPpCt5X

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.

1.881 × 10¹⁰⁷(108-digit number)

18814635338889397537…84416188878019918979

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

1.881 × 10¹⁰⁷(108-digit number)

18814635338889397537…84416188878019918979

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.881 × 10¹⁰⁷(108-digit number)

18814635338889397537…84416188878019918981

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

3.762 × 10¹⁰⁷(108-digit number)

37629270677778795074…68832377756039837959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.762 × 10¹⁰⁷(108-digit number)

37629270677778795074…68832377756039837961

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

7.525 × 10¹⁰⁷(108-digit number)

75258541355557590148…37664755512079675919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.525 × 10¹⁰⁷(108-digit number)

75258541355557590148…37664755512079675921

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

1.505 × 10¹⁰⁸(109-digit number)

15051708271111518029…75329511024159351839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.505 × 10¹⁰⁸(109-digit number)

15051708271111518029…75329511024159351841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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