Home/Chain Registry/Block #457,163

Block #457,163

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 5:05:26 PM · Difficulty 10.4212 · 6,333,872 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

74ebe35e466ca6f7c663cafc89e3fb93722609cbbbb6b8d5854a4387e823440d

View on Chainz ↗

Height

#457,163

Difficulty

10.421208

Transactions

Size

208 B

Version

Bits

0a6bd443

Nonce

333,690

Timestamp

3/23/2014, 5:05:26 PM

Confirmations

6,333,872

Merkle Root

8e6b9b225c4db3365db540dd7224e17b732860b17aa91741fa6b6bdf5e88cfe6

Transactions (1)

Coinbase8e6b9b225c4db3…6b6bdf5e88cfe6

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

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.

2.369 × 10⁹⁸(99-digit number)

23695728922988730811…11762874397480332580

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

2.369 × 10⁹⁸(99-digit number)

23695728922988730811…11762874397480332579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.369 × 10⁹⁸(99-digit number)

23695728922988730811…11762874397480332581

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

4.739 × 10⁹⁸(99-digit number)

47391457845977461623…23525748794960665159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.739 × 10⁹⁸(99-digit number)

47391457845977461623…23525748794960665161

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

9.478 × 10⁹⁸(99-digit number)

94782915691954923247…47051497589921330319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.478 × 10⁹⁸(99-digit number)

94782915691954923247…47051497589921330321

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

1.895 × 10⁹⁹(100-digit number)

18956583138390984649…94102995179842660639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.895 × 10⁹⁹(100-digit number)

18956583138390984649…94102995179842660641

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

3.791 × 10⁹⁹(100-digit number)

37913166276781969298…88205990359685321279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.791 × 10⁹⁹(100-digit number)

37913166276781969298…88205990359685321281

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 457163

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 74ebe35e466ca6f7c663cafc89e3fb93722609cbbbb6b8d5854a4387e823440d

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 #457,163 on Chainz ↗