Home/Chain Registry/Block #48,264

Block #48,264

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/15/2013, 2:33:50 PM · Difficulty 8.8408 · 6,741,737 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fd99dc6818e2216007c30a25187cebec2cab9a5f96bca754e239ae8c81ccef9a

View on Chainz ↗

Height

#48,264

Difficulty

8.840837

Transactions

Size

2.15 KB

Version

Bits

08d74120

Nonce

Timestamp

7/15/2013, 2:33:50 PM

Confirmations

6,741,737

Merkle Root

cdaa6f9817336012e40a4d021fdca977f95ba5983a14e86e32b9ac15b2a5a280

Transactions (2)

Coinbased4f01b2b7d2846…c5c007bfde841e

1 in → 1 out12.8100 XPM110 B

Ac9FAiLX…y5M5E5hz

e82f33a8259b80…779ee9e68ee736

13 in → 2 out300.0100 XPM1.95 KB

ANokenZx…sNgASSEm ASmAWZM6…QycdGfzx

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.

5.437 × 10¹⁰⁰(101-digit number)

54375909425825494418…61512469244426932250

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

5.437 × 10¹⁰⁰(101-digit number)

54375909425825494418…61512469244426932249

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.437 × 10¹⁰⁰(101-digit number)

54375909425825494418…61512469244426932251

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

1.087 × 10¹⁰¹(102-digit number)

10875181885165098883…23024938488853864499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.087 × 10¹⁰¹(102-digit number)

10875181885165098883…23024938488853864501

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

2.175 × 10¹⁰¹(102-digit number)

21750363770330197767…46049876977707728999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.175 × 10¹⁰¹(102-digit number)

21750363770330197767…46049876977707729001

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

4.350 × 10¹⁰¹(102-digit number)

43500727540660395535…92099753955415457999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.350 × 10¹⁰¹(102-digit number)

43500727540660395535…92099753955415458001

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

8.700 × 10¹⁰¹(102-digit number)

87001455081320791070…84199507910830915999

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 48264

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 fd99dc6818e2216007c30a25187cebec2cab9a5f96bca754e239ae8c81ccef9a

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 #48,264 on Chainz ↗