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Block #478,703

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/7/2014, 6:12:35 AM · Difficulty 10.4959 · 6,335,301 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1329b06d26744ffdc3574d90f58c19870a8550d783eacfa8c170f4e9bb588f6a

View on Chainz ↗

Height

#478,703

Difficulty

10.495896

Transactions

Size

883 B

Version

Bits

0a7ef307

Nonce

2,590

Timestamp

4/7/2014, 6:12:35 AM

Confirmations

6,335,301

Merkle Root

215cc66f231e2f56592599c941560ed780357e5ff5e93f4d1e388f990cc1e198

Transactions (4)

Coinbase3cf4178e504532…2b779360fc0c6a

1 in → 1 out9.0900 XPM112 B

AN6uQEbp…cUYMq9yM

383b055cf6e80c…ecd6a9a2bcf340

1 in → 2 out6.5704 XPM226 B

AcMAjQV3…W7ko5s18 APS4PAas…U6aXoPX5

7e994c491ad3d4…97eabf7211bab8

1 in → 2 out5.8429 XPM226 B

AerrjcNc…QPu2sGrj AWQfJ47C…7YWaXq1C

a47c4d958f19c0…9b0caffb6a2e3a

1 in → 2 out3.4779 XPM227 B

AZzQaDhq…iJVS81jy AHBSCedt…p9vKvAas

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.

6.654 × 10⁹⁸(99-digit number)

66540528566899208916…78061448546567548800

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

6.654 × 10⁹⁸(99-digit number)

66540528566899208916…78061448546567548799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.654 × 10⁹⁸(99-digit number)

66540528566899208916…78061448546567548801

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

1.330 × 10⁹⁹(100-digit number)

13308105713379841783…56122897093135097599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.330 × 10⁹⁹(100-digit number)

13308105713379841783…56122897093135097601

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

2.661 × 10⁹⁹(100-digit number)

26616211426759683566…12245794186270195199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.661 × 10⁹⁹(100-digit number)

26616211426759683566…12245794186270195201

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

5.323 × 10⁹⁹(100-digit number)

53232422853519367132…24491588372540390399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.323 × 10⁹⁹(100-digit number)

53232422853519367132…24491588372540390401

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

1.064 × 10¹⁰⁰(101-digit number)

10646484570703873426…48983176745080780799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.064 × 10¹⁰⁰(101-digit number)

10646484570703873426…48983176745080780801

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 478703

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 1329b06d26744ffdc3574d90f58c19870a8550d783eacfa8c170f4e9bb588f6a

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 #478,703 on Chainz ↗

Block #478,703

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