Block #508,562

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/24/2014, 11:23:56 AM · Difficulty 10.8190 · 6,309,350 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de34613030790473f81bd9f98486ae55dd9f3fe81c4d9bacaa5d3471cfcd8ca7

View on Chainz ↗

Height

#508,562

Difficulty

10.818960

Transactions

Size

2.74 KB

Version

Bits

0ad1a755

Nonce

28,844,895

Timestamp

4/24/2014, 11:23:56 AM

Confirmations

6,309,350

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ca3b98f0dbb5537cfa305a8bf6e9dbe5641f559b8d9573872a21dd3b93fbfccb

Transactions (2)

Coinbasecfa8b7588bee7c…d649af6702fd0c

1 in → 1 out8.5600 XPM116 B

AbwWkWZt…kawDhufa

9779e6a150ab64…a9b3cd2246cfd5

17 in → 2 out17.1699 XPM2.53 KB

AXnXEwg6…un9Teu49 Ab9qnCLr…SKRWozzU

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.

2.824 × 10⁹⁹(100-digit number)

28245618578526847414…19828190256560520959

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

2.824 × 10⁹⁹(100-digit number)

28245618578526847414…19828190256560520959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.824 × 10⁹⁹(100-digit number)

28245618578526847414…19828190256560520961

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

5.649 × 10⁹⁹(100-digit number)

56491237157053694828…39656380513121041919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.649 × 10⁹⁹(100-digit number)

56491237157053694828…39656380513121041921

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

1.129 × 10¹⁰⁰(101-digit number)

11298247431410738965…79312761026242083839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.129 × 10¹⁰⁰(101-digit number)

11298247431410738965…79312761026242083841

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

2.259 × 10¹⁰⁰(101-digit number)

22596494862821477931…58625522052484167679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.259 × 10¹⁰⁰(101-digit number)

22596494862821477931…58625522052484167681

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

4.519 × 10¹⁰⁰(101-digit number)

45192989725642955862…17251044104968335359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.519 × 10¹⁰⁰(101-digit number)

45192989725642955862…17251044104968335361

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #508,562

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