Home/Chain Registry/Block #284,723

Block #284,723

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 5:38:27 AM · Difficulty 9.9832 · 6,515,799 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

07ee212ab5bae1f4eae510a9cb3776b52d5407e2267b5297a308447c82ebb23c

View on Chainz ↗

Height

#284,723

Difficulty

9.983204

Transactions

Size

1.18 KB

Version

Bits

09fbb345

Nonce

119,147

Timestamp

11/30/2013, 5:38:27 AM

Confirmations

6,515,799

Merkle Root

b3dd85c211e14b664a178d93fd83411cc5b18b3bf6a98a6ba25f4ac38ab90f97

Transactions (1)

Coinbaseb3dd85c211e14b…5f4ac38ab90f97

1 in → 31 out10.0000 XPM1.09 KB

Ad9pSzHt…cpJ3y2zz AKde1i4d…88R1bw6g AXeQnyEs…fUWKQwq8 Acs9SHrk…QJSB8SFG AREvLX4V…M5PNeLVD

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.

3.826 × 10⁹⁵(96-digit number)

38269701019352089424…25054397787463766400

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

3.826 × 10⁹⁵(96-digit number)

38269701019352089424…25054397787463766399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.826 × 10⁹⁵(96-digit number)

38269701019352089424…25054397787463766401

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

7.653 × 10⁹⁵(96-digit number)

76539402038704178849…50108795574927532799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.653 × 10⁹⁵(96-digit number)

76539402038704178849…50108795574927532801

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

1.530 × 10⁹⁶(97-digit number)

15307880407740835769…00217591149855065599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.530 × 10⁹⁶(97-digit number)

15307880407740835769…00217591149855065601

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

3.061 × 10⁹⁶(97-digit number)

30615760815481671539…00435182299710131199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.061 × 10⁹⁶(97-digit number)

30615760815481671539…00435182299710131201

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

6.123 × 10⁹⁶(97-digit number)

61231521630963343079…00870364599420262399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.123 × 10⁹⁶(97-digit number)

61231521630963343079…00870364599420262401

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 284723

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 07ee212ab5bae1f4eae510a9cb3776b52d5407e2267b5297a308447c82ebb23c

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 #284,723 on Chainz ↗