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Block #506,844

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2014, 8:29:49 AM · Difficulty 10.8152 · 6,320,272 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dfbfb4cd10a7b46ee60b09d8cdf6f0ce0b4429b1b5745eead0f44e680d608b08

View on Chainz ↗

Height

#506,844

Difficulty

10.815208

Transactions

Size

414 B

Version

Bits

0ad0b17a

Nonce

105,435

Timestamp

4/23/2014, 8:29:49 AM

Confirmations

6,320,272

Merkle Root

9e5814da42d65cd37f7df10854e1e45a88ac24d43f1eaa88001f1907d9608400

Transactions (2)

Coinbase86b018f23f0a52…58ca5e769429db

1 in → 1 out8.5400 XPM97 B

AKxxLGqh…oySJc6b5

2442edb651b190…419990eb02cab1

1 in → 2 out2.2491 XPM225 B

ASoUJCPN…QY3u51ED AFvwLqTg…vsLvKXNM

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.

1.681 × 10⁹⁹(100-digit number)

16819198543330167376…72199091451619974720

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

1.681 × 10⁹⁹(100-digit number)

16819198543330167376…72199091451619974719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.681 × 10⁹⁹(100-digit number)

16819198543330167376…72199091451619974721

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

3.363 × 10⁹⁹(100-digit number)

33638397086660334752…44398182903239949439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.363 × 10⁹⁹(100-digit number)

33638397086660334752…44398182903239949441

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

6.727 × 10⁹⁹(100-digit number)

67276794173320669505…88796365806479898879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.727 × 10⁹⁹(100-digit number)

67276794173320669505…88796365806479898881

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

1.345 × 10¹⁰⁰(101-digit number)

13455358834664133901…77592731612959797759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.345 × 10¹⁰⁰(101-digit number)

13455358834664133901…77592731612959797761

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

2.691 × 10¹⁰⁰(101-digit number)

26910717669328267802…55185463225919595519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.691 × 10¹⁰⁰(101-digit number)

26910717669328267802…55185463225919595521

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 506844

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 dfbfb4cd10a7b46ee60b09d8cdf6f0ce0b4429b1b5745eead0f44e680d608b08

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 #506,844 on Chainz ↗

Block #506,844

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