Home/Chain Registry/Block #430,615

Block #430,615

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/5/2014, 2:56:51 PM · Difficulty 10.3450 · 6,381,144 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f559eaf02ab239be0bb418f4e48306dda9a9e271c88a6b25f846534c7aba4bfa

View on Chainz ↗

Height

#430,615

Difficulty

10.345034

Transactions

Size

433 B

Version

Bits

0a585429

Nonce

15,830

Timestamp

3/5/2014, 2:56:51 PM

Confirmations

6,381,144

Merkle Root

5a2fbc0ff8ef06c37914072acad1b5b1848d4b1af2631153d4cc729719808e55

Transactions (2)

Coinbase63ad94548533f8…a02daa76db3015

1 in → 1 out9.3400 XPM116 B

AbwWkWZt…kawDhufa

3760114b601169…fdb6059786da6c

1 in → 2 out4800.7374 XPM225 B

AdyU4qQL…DDVCs6eb APvMG9X2…VbTpQLrt

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.

5.593 × 10⁹⁹(100-digit number)

55931071179239811316…36398256775622218760

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

5.593 × 10⁹⁹(100-digit number)

55931071179239811316…36398256775622218759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.593 × 10⁹⁹(100-digit number)

55931071179239811316…36398256775622218761

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

1.118 × 10¹⁰⁰(101-digit number)

11186214235847962263…72796513551244437519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.118 × 10¹⁰⁰(101-digit number)

11186214235847962263…72796513551244437521

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

2.237 × 10¹⁰⁰(101-digit number)

22372428471695924526…45593027102488875039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.237 × 10¹⁰⁰(101-digit number)

22372428471695924526…45593027102488875041

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

4.474 × 10¹⁰⁰(101-digit number)

44744856943391849053…91186054204977750079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.474 × 10¹⁰⁰(101-digit number)

44744856943391849053…91186054204977750081

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

8.948 × 10¹⁰⁰(101-digit number)

89489713886783698106…82372108409955500159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.948 × 10¹⁰⁰(101-digit number)

89489713886783698106…82372108409955500161

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 430615

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 f559eaf02ab239be0bb418f4e48306dda9a9e271c88a6b25f846534c7aba4bfa

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 #430,615 on Chainz ↗

Block #430,615

Cookie Preferences