Home/Chain Registry/Block #469,117

Block #469,117

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/31/2014, 11:58:07 PM · Difficulty 10.4303 · 6,334,311 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d7052d9eccb12d28d7df4e00a404efc7d68372ea76cf69acce570c165f28036b

View on Chainz ↗

Height

#469,117

Difficulty

10.430336

Transactions

Size

1004 B

Version

Bits

0a6e2a81

Nonce

108,241

Timestamp

3/31/2014, 11:58:07 PM

Confirmations

6,334,311

Merkle Root

9b15767785e9b4096468004438402765ef79b0f107c10085ae32edc31eb7bce3

Transactions (1)

Coinbase9b15767785e9b4…32edc31eb7bce3

1 in → 25 out9.1800 XPM913 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 AMm3qeod…8PBiCMXU

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.

6.530 × 10⁹⁵(96-digit number)

65303646634489006332…27438672346771963860

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

6.530 × 10⁹⁵(96-digit number)

65303646634489006332…27438672346771963859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.530 × 10⁹⁵(96-digit number)

65303646634489006332…27438672346771963861

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

1.306 × 10⁹⁶(97-digit number)

13060729326897801266…54877344693543927719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.306 × 10⁹⁶(97-digit number)

13060729326897801266…54877344693543927721

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

2.612 × 10⁹⁶(97-digit number)

26121458653795602533…09754689387087855439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.612 × 10⁹⁶(97-digit number)

26121458653795602533…09754689387087855441

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

5.224 × 10⁹⁶(97-digit number)

52242917307591205066…19509378774175710879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.224 × 10⁹⁶(97-digit number)

52242917307591205066…19509378774175710881

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

1.044 × 10⁹⁷(98-digit number)

10448583461518241013…39018757548351421759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.044 × 10⁹⁷(98-digit number)

10448583461518241013…39018757548351421761

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 469117

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 d7052d9eccb12d28d7df4e00a404efc7d68372ea76cf69acce570c165f28036b

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 #469,117 on Chainz ↗