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Block #513,026

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/27/2014, 6:23:52 AM · Difficulty 10.8344 · 6,314,143 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b9bc1ebc5d5974fe30183f06e74ebbfce2cfb23bb42de3ea01c8b5721b4a1b71

View on Chainz ↗

Height

#513,026

Difficulty

10.834414

Transactions

Size

209 B

Version

Bits

0ad59c24

Nonce

100,937,815

Timestamp

4/27/2014, 6:23:52 AM

Confirmations

6,314,143

Merkle Root

ae3af8afc6102be5b6792d8a1bc5344e937fd4c408392c0cb7ce364227b557d8

Transactions (1)

Coinbaseae3af8afc6102b…ce364227b557d8

1 in → 1 out8.5100 XPM116 B

AbwWkWZt…kawDhufa

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.

1.822 × 10¹⁰¹(102-digit number)

18228119554911662041…27460725269945497600

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

1.822 × 10¹⁰¹(102-digit number)

18228119554911662041…27460725269945497599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.822 × 10¹⁰¹(102-digit number)

18228119554911662041…27460725269945497601

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

3.645 × 10¹⁰¹(102-digit number)

36456239109823324082…54921450539890995199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.645 × 10¹⁰¹(102-digit number)

36456239109823324082…54921450539890995201

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

7.291 × 10¹⁰¹(102-digit number)

72912478219646648165…09842901079781990399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.291 × 10¹⁰¹(102-digit number)

72912478219646648165…09842901079781990401

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

1.458 × 10¹⁰²(103-digit number)

14582495643929329633…19685802159563980799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.458 × 10¹⁰²(103-digit number)

14582495643929329633…19685802159563980801

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

2.916 × 10¹⁰²(103-digit number)

29164991287858659266…39371604319127961599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.916 × 10¹⁰²(103-digit number)

29164991287858659266…39371604319127961601

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

5.832 × 10¹⁰²(103-digit number)

58329982575717318532…78743208638255923199

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 513026

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 b9bc1ebc5d5974fe30183f06e74ebbfce2cfb23bb42de3ea01c8b5721b4a1b71

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 #513,026 on Chainz ↗

Block #513,026

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