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Block #2,754,435

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/18/2018, 12:20:21 PM · Difficulty 11.6572 · 4,088,173 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b475a13a9a0c474b595551e77ee9931ff49b04dbc74b9e04e46fe9cba50d483b

View on Chainz ↗

Height

#2,754,435

Difficulty

11.657155

Transactions

Size

199 B

Version

Bits

0ba83b47

Nonce

481,795,754

Timestamp

7/18/2018, 12:20:21 PM

Confirmations

4,088,173

Merkle Root

73a47f4cb6d55ea2dc569dc88cf27eb465ef201acaefe2de082bd9db1b4e6477

Transactions (1)

Coinbase73a47f4cb6d55e…2bd9db1b4e6477

1 in → 1 out7.3500 XPM110 B

AbqTTVkY…S8n4YhAm

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.

1.695 × 10⁹²(93-digit number)

16953378212158040749…79954604863587930880

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

1.695 × 10⁹²(93-digit number)

16953378212158040749…79954604863587930879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.695 × 10⁹²(93-digit number)

16953378212158040749…79954604863587930881

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

3.390 × 10⁹²(93-digit number)

33906756424316081499…59909209727175861759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.390 × 10⁹²(93-digit number)

33906756424316081499…59909209727175861761

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

6.781 × 10⁹²(93-digit number)

67813512848632162998…19818419454351723519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.781 × 10⁹²(93-digit number)

67813512848632162998…19818419454351723521

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

1.356 × 10⁹³(94-digit number)

13562702569726432599…39636838908703447039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.356 × 10⁹³(94-digit number)

13562702569726432599…39636838908703447041

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

2.712 × 10⁹³(94-digit number)

27125405139452865199…79273677817406894079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.712 × 10⁹³(94-digit number)

27125405139452865199…79273677817406894081

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

5.425 × 10⁹³(94-digit number)

54250810278905730399…58547355634813788159

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 2754435

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 b475a13a9a0c474b595551e77ee9931ff49b04dbc74b9e04e46fe9cba50d483b

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 #2,754,435 on Chainz ↗

Block #2,754,435

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