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Block #578,515

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/6/2014, 2:58:07 AM · Difficulty 10.9682 · 6,234,202 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1abefbae1cc3f793e01e19a1bc551b0e1e919cc5a25521f485fc43fa7e248beb

View on Chainz ↗

Height

#578,515

Difficulty

10.968177

Transactions

Size

207 B

Version

Bits

0af7da79

Nonce

2,137,718,687

Timestamp

6/6/2014, 2:58:07 AM

Confirmations

6,234,202

Merkle Root

95e89497552bc1439e2bd5eadff6296c7c64d1d65d89923608072d5e0e7633dc

Transactions (1)

Coinbase95e89497552bc1…072d5e0e7633dc

1 in → 1 out8.3000 XPM116 B

ANSXnLY2…Sd25TjkD

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.

2.622 × 10⁹⁷(98-digit number)

26225301936204086040…61535378129561350240

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

2.622 × 10⁹⁷(98-digit number)

26225301936204086040…61535378129561350239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.622 × 10⁹⁷(98-digit number)

26225301936204086040…61535378129561350241

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

5.245 × 10⁹⁷(98-digit number)

52450603872408172080…23070756259122700479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.245 × 10⁹⁷(98-digit number)

52450603872408172080…23070756259122700481

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

1.049 × 10⁹⁸(99-digit number)

10490120774481634416…46141512518245400959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.049 × 10⁹⁸(99-digit number)

10490120774481634416…46141512518245400961

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

2.098 × 10⁹⁸(99-digit number)

20980241548963268832…92283025036490801919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.098 × 10⁹⁸(99-digit number)

20980241548963268832…92283025036490801921

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

4.196 × 10⁹⁸(99-digit number)

41960483097926537664…84566050072981603839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.196 × 10⁹⁸(99-digit number)

41960483097926537664…84566050072981603841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

8.392 × 10⁹⁸(99-digit number)

83920966195853075328…69132100145963207679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 578515

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 1abefbae1cc3f793e01e19a1bc551b0e1e919cc5a25521f485fc43fa7e248beb

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 #578,515 on Chainz ↗

Block #578,515

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