Home/Chain Registry/Block #475,320

Block #475,320

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 4:06:54 AM · Difficulty 10.4556 · 6,320,857 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f044bca680ef6bb2b102f6635098abbd0bae5e010fcf802857ceefc17b00bd9a

View on Chainz ↗

Height

#475,320

Difficulty

10.455575

Transactions

Size

1004 B

Version

Bits

0a74a08e

Nonce

44,368

Timestamp

4/5/2014, 4:06:54 AM

Confirmations

6,320,857

Merkle Root

07ab58e585ba324adc5e22b8b4bf768ea5401568efb6837e27d9f82ec8c013d3

Transactions (1)

Coinbase07ab58e585ba32…d9f82ec8c013d3

1 in → 25 out9.1300 XPM913 B

AGz9gyZW…bo8NYQpw AdFLJFhb…bsaVkAyh AUFKXvnz…342ApNcm ATp4jJhs…TbSgR8Qb AZr7Ptuw…CM4Yw5jq

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.

8.759 × 10⁹⁷(98-digit number)

87590066226141685895…07513010433755469440

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

8.759 × 10⁹⁷(98-digit number)

87590066226141685895…07513010433755469439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.759 × 10⁹⁷(98-digit number)

87590066226141685895…07513010433755469441

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

1.751 × 10⁹⁸(99-digit number)

17518013245228337179…15026020867510938879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.751 × 10⁹⁸(99-digit number)

17518013245228337179…15026020867510938881

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

3.503 × 10⁹⁸(99-digit number)

35036026490456674358…30052041735021877759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.503 × 10⁹⁸(99-digit number)

35036026490456674358…30052041735021877761

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

7.007 × 10⁹⁸(99-digit number)

70072052980913348716…60104083470043755519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.007 × 10⁹⁸(99-digit number)

70072052980913348716…60104083470043755521

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

1.401 × 10⁹⁹(100-digit number)

14014410596182669743…20208166940087511039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.401 × 10⁹⁹(100-digit number)

14014410596182669743…20208166940087511041

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 475320

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 f044bca680ef6bb2b102f6635098abbd0bae5e010fcf802857ceefc17b00bd9a

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 #475,320 on Chainz ↗