Block #52,919

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/16/2013, 12:46:39 PM · Difficulty 8.9178 · 6,738,074 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6845683b8cb8fa591701da5bcc5b18836ffd8e9b32c659a7d19a6b49703728c8

View on Chainz ↗

Height

#52,919

Difficulty

8.917767

Transactions

Size

205 B

Version

Bits

08eaf2cd

Nonce

313

Timestamp

7/16/2013, 12:46:39 PM

Confirmations

6,738,074

Merkle Root

dda4bfe684464656ac607faa3ed1c9ebeb8f0e282fdb60868fdee55e9b71aa33

Transactions (1)

Coinbasedda4bfe6844646…dee55e9b71aa33

1 in → 1 out12.5600 XPM110 B

AeTcmmqH…LrFchfe1

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.

1.572 × 10¹⁰⁷(108-digit number)

15726057403979939487…55923662381638566479

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

1.572 × 10¹⁰⁷(108-digit number)

15726057403979939487…55923662381638566479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.572 × 10¹⁰⁷(108-digit number)

15726057403979939487…55923662381638566481

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

3.145 × 10¹⁰⁷(108-digit number)

31452114807959878975…11847324763277132959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.145 × 10¹⁰⁷(108-digit number)

31452114807959878975…11847324763277132961

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

6.290 × 10¹⁰⁷(108-digit number)

62904229615919757950…23694649526554265919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.290 × 10¹⁰⁷(108-digit number)

62904229615919757950…23694649526554265921

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

1.258 × 10¹⁰⁸(109-digit number)

12580845923183951590…47389299053108531839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.258 × 10¹⁰⁸(109-digit number)

12580845923183951590…47389299053108531841

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