Home/Chain Registry/Block #429,829

Block #429,829

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/5/2014, 2:12:36 AM · Difficulty 10.3420 · 6,371,867 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a701e7e959b9afd4e6fa938b7cc355b1f1b8295a3ddbf3c9edcf190e4801866f

View on Chainz ↗

Height

#429,829

Difficulty

10.341987

Transactions

Size

203 B

Version

Bits

0a578c7a

Nonce

185,976

Timestamp

3/5/2014, 2:12:36 AM

Confirmations

6,371,867

Merkle Root

755fc8216e510b23b6f900723b191abd8a3e862fd12ec0352ce8e64f91a085b7

Transactions (1)

Coinbase755fc8216e510b…e8e64f91a085b7

1 in → 1 out9.3400 XPM110 B

AeKNrjNj…1NEq95Ta

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.

1.075 × 10¹⁰¹(102-digit number)

10758525221907900479…34532374886890092800

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

1.075 × 10¹⁰¹(102-digit number)

10758525221907900479…34532374886890092799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.075 × 10¹⁰¹(102-digit number)

10758525221907900479…34532374886890092801

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

2.151 × 10¹⁰¹(102-digit number)

21517050443815800959…69064749773780185599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.151 × 10¹⁰¹(102-digit number)

21517050443815800959…69064749773780185601

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

4.303 × 10¹⁰¹(102-digit number)

43034100887631601918…38129499547560371199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.303 × 10¹⁰¹(102-digit number)

43034100887631601918…38129499547560371201

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

8.606 × 10¹⁰¹(102-digit number)

86068201775263203837…76258999095120742399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.606 × 10¹⁰¹(102-digit number)

86068201775263203837…76258999095120742401

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

1.721 × 10¹⁰²(103-digit number)

17213640355052640767…52517998190241484799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.721 × 10¹⁰²(103-digit number)

17213640355052640767…52517998190241484801

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 429829

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 a701e7e959b9afd4e6fa938b7cc355b1f1b8295a3ddbf3c9edcf190e4801866f

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 #429,829 on Chainz ↗