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Block #358,493

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/14/2014, 3:26:31 AM · Difficulty 10.3865 · 6,432,710 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

191f978e1c6cd4891516882af7577024108cff329d48f343ea818ba07d638aab

View on Chainz ↗

Height

#358,493

Difficulty

10.386498

Transactions

Size

1.08 KB

Version

Bits

0a62f182

Nonce

15,237

Timestamp

1/14/2014, 3:26:31 AM

Confirmations

6,432,710

Merkle Root

440b2eab44b50b542b4abff3f45c0206d5cdf4aaf32ea2c61a3cdd69a16e2592

Transactions (1)

Coinbase440b2eab44b50b…3cdd69a16e2592

1 in → 28 out9.2400 XPM1015 B

Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AbdRzKzS…idvq53mH Ad9pSzHt…cpJ3y2zz Ac7TsAMG…2W5MRTA8

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.

9.838 × 10¹⁰³(104-digit number)

98383230120088353654…69397902584218176160

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

9.838 × 10¹⁰³(104-digit number)

98383230120088353654…69397902584218176159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.838 × 10¹⁰³(104-digit number)

98383230120088353654…69397902584218176161

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

1.967 × 10¹⁰⁴(105-digit number)

19676646024017670730…38795805168436352319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.967 × 10¹⁰⁴(105-digit number)

19676646024017670730…38795805168436352321

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

3.935 × 10¹⁰⁴(105-digit number)

39353292048035341461…77591610336872704639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.935 × 10¹⁰⁴(105-digit number)

39353292048035341461…77591610336872704641

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

7.870 × 10¹⁰⁴(105-digit number)

78706584096070682923…55183220673745409279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.870 × 10¹⁰⁴(105-digit number)

78706584096070682923…55183220673745409281

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

1.574 × 10¹⁰⁵(106-digit number)

15741316819214136584…10366441347490818559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.574 × 10¹⁰⁵(106-digit number)

15741316819214136584…10366441347490818561

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 358493

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 191f978e1c6cd4891516882af7577024108cff329d48f343ea818ba07d638aab

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 #358,493 on Chainz ↗