Home/Chain Registry/Block #268,467

Block #268,467

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/22/2013, 4:05:46 AM · Difficulty 9.9571 · 6,533,001 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b9e6463d1fbdf2e599ec68c0f51ff05a247e9ebae0c4142f9a0761d586b1b7c3

View on Chainz ↗

Height

#268,467

Difficulty

9.957052

Transactions

Size

235 B

Version

Bits

09f5015c

Nonce

5,214

Timestamp

11/22/2013, 4:05:46 AM

Confirmations

6,533,001

Merkle Root

0e071a505e6971438bf5d74a938fc7e47bcba944e4ebad54696eb511d4035344

Transactions (1)

Coinbase0e071a505e6971…6eb511d4035344

1 in → 2 out10.0700 XPM142 B

AdGRRh1e…QmctLb24 ALfEGCwh…VawujfMm

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.

1.722 × 10¹⁰²(103-digit number)

17222854901556287883…87819378718563125060

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

1.722 × 10¹⁰²(103-digit number)

17222854901556287883…87819378718563125059

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.722 × 10¹⁰²(103-digit number)

17222854901556287883…87819378718563125061

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

3.444 × 10¹⁰²(103-digit number)

34445709803112575766…75638757437126250119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.444 × 10¹⁰²(103-digit number)

34445709803112575766…75638757437126250121

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

6.889 × 10¹⁰²(103-digit number)

68891419606225151533…51277514874252500239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.889 × 10¹⁰²(103-digit number)

68891419606225151533…51277514874252500241

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

1.377 × 10¹⁰³(104-digit number)

13778283921245030306…02555029748505000479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.377 × 10¹⁰³(104-digit number)

13778283921245030306…02555029748505000481

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

2.755 × 10¹⁰³(104-digit number)

27556567842490060613…05110059497010000959

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 268467

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 b9e6463d1fbdf2e599ec68c0f51ff05a247e9ebae0c4142f9a0761d586b1b7c3

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 #268,467 on Chainz ↗