Home/Chain Registry/Block #52,130

Block #52,130

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/16/2013, 8:57:53 AM · Difficulty 8.9081 · 6,760,080 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e40fd6ee1417b3000131341ed42f55087834954e115cf36dcc717c4e86c8d732

View on Chainz ↗

Height

#52,130

Difficulty

8.908071

Transactions

Size

204 B

Version

Bits

08e8775a

Nonce

727

Timestamp

7/16/2013, 8:57:53 AM

Confirmations

6,760,080

Merkle Root

136e13e2dc78327e0afe4ec70844fe171edcbd127ec437cd10dfd80ecc4ba276

Transactions (1)

Coinbase136e13e2dc7832…dfd80ecc4ba276

1 in → 1 out12.5800 XPM109 B

AbjxNDBu…YEKumYSF

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.

2.383 × 10¹⁰⁷(108-digit number)

23830297453395142781…82203015094065938870

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

2.383 × 10¹⁰⁷(108-digit number)

23830297453395142781…82203015094065938869

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.383 × 10¹⁰⁷(108-digit number)

23830297453395142781…82203015094065938871

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

4.766 × 10¹⁰⁷(108-digit number)

47660594906790285563…64406030188131877739

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.766 × 10¹⁰⁷(108-digit number)

47660594906790285563…64406030188131877741

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

9.532 × 10¹⁰⁷(108-digit number)

95321189813580571126…28812060376263755479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.532 × 10¹⁰⁷(108-digit number)

95321189813580571126…28812060376263755481

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

1.906 × 10¹⁰⁸(109-digit number)

19064237962716114225…57624120752527510959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.906 × 10¹⁰⁸(109-digit number)

19064237962716114225…57624120752527510961

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

3.812 × 10¹⁰⁸(109-digit number)

38128475925432228450…15248241505055021919

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 52130

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 e40fd6ee1417b3000131341ed42f55087834954e115cf36dcc717c4e86c8d732

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 #52,130 on Chainz ↗

Block #52,130

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