Home/Chain Registry/Block #470,848

Block #470,848

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/2/2014, 5:18:19 AM · Difficulty 10.4285 · 6,328,308 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1bb201366aefea0385a6bf875f226e60c62e574b68355d96aeea58c7d03cab17

View on Chainz ↗

Height

#470,848

Difficulty

10.428476

Transactions

Size

1.17 KB

Version

Bits

0a6db09b

Nonce

23,139

Timestamp

4/2/2014, 5:18:19 AM

Confirmations

6,328,308

Merkle Root

ad8eeaaf9f9738f26f004fd36f21b13c358abb358f7a1ba3c8f51e6902bfae20

Transactions (2)

Coinbase474be3150c180d…d7a942f9417ee0

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

8941cb538fa163…2be6240a7be5c9

5 in → 10 out30.7480 XPM989 B

AWTZZcwE…FiMgXUJV ASLVz6ep…wadJNQxR AaNiudXg…eLkWQWr4 AeqZw9yo…5K9AMCop AXbbkuVv…UixHY7hn

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.

3.009 × 10¹⁰³(104-digit number)

30097039834359083376…27015376151411138240

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

3.009 × 10¹⁰³(104-digit number)

30097039834359083376…27015376151411138239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.009 × 10¹⁰³(104-digit number)

30097039834359083376…27015376151411138241

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

6.019 × 10¹⁰³(104-digit number)

60194079668718166752…54030752302822276479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.019 × 10¹⁰³(104-digit number)

60194079668718166752…54030752302822276481

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

1.203 × 10¹⁰⁴(105-digit number)

12038815933743633350…08061504605644552959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.203 × 10¹⁰⁴(105-digit number)

12038815933743633350…08061504605644552961

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

2.407 × 10¹⁰⁴(105-digit number)

24077631867487266700…16123009211289105919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.407 × 10¹⁰⁴(105-digit number)

24077631867487266700…16123009211289105921

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

4.815 × 10¹⁰⁴(105-digit number)

48155263734974533401…32246018422578211839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.815 × 10¹⁰⁴(105-digit number)

48155263734974533401…32246018422578211841

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.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 470848

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 1bb201366aefea0385a6bf875f226e60c62e574b68355d96aeea58c7d03cab17

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #470,848 on Chainz ↗