Home/Chain Registry/Block #2,789,393

Block #2,789,393

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 8/11/2018, 3:32:12 PM · Difficulty 11.6721 · 4,053,441 confirmations

2CC

Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header

Block Hash

f5c0ecc895fb9397c830ff8362c577dd7399c922f8145151c05336a996fea5e4

View on Chainz ↗

Height

#2,789,393

Difficulty

11.672071

Transactions

Size

776 B

Version

Bits

0bac0ce0

Nonce

195,294,873

Timestamp

8/11/2018, 3:32:12 PM

Confirmations

4,053,441

Merkle Root

fe1dc6c1129e4224210971334c985b790b9c6a2077460714ffcf7379a15e0af5

Transactions (4)

Coinbasebd9bc6ca61d06f…720d7a95f3c6f7

1 in → 1 out7.3600 XPM110 B

AZtxQr2F…7grUWrUz

52ef6d0986fa5b…c0cb5e571b3a1f

1 in → 2 out7.3200 XPM192 B

ARzQNAct…Ve8WbCMT ASRS2VU5…28AUNG3z

5e3d290762a7bc…e95c9e6a4c41a4

1 in → 2 out7.3200 XPM193 B

AUumBS5d…FjQqjZGK AUPyFBKY…KZL6NMKo

651e57cbbe2b2c…c2e43675bacc2c

1 in → 2 out7.3200 XPM191 B

AHcau61b…qScAzNWb AS6BfMDx…yWVBQAXY

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.

4.796 × 10⁹⁵(96-digit number)

47968491001165159988…39932996901948172800

Discovered Prime Numbers

p_k = 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.

origin + 1

4.796 × 10⁹⁵(96-digit number)

47968491001165159988…39932996901948172801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

9.593 × 10⁹⁵(96-digit number)

95936982002330319977…79865993803896345601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.918 × 10⁹⁶(97-digit number)

19187396400466063995…59731987607792691201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.837 × 10⁹⁶(97-digit number)

38374792800932127990…19463975215585382401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.674 × 10⁹⁶(97-digit number)

76749585601864255981…38927950431170764801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.534 × 10⁹⁷(98-digit number)

15349917120372851196…77855900862341529601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.069 × 10⁹⁷(98-digit number)

30699834240745702392…55711801724683059201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.139 × 10⁹⁷(98-digit number)

61399668481491404785…11423603449366118401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.227 × 10⁹⁸(99-digit number)

12279933696298280957…22847206898732236801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.455 × 10⁹⁸(99-digit number)

24559867392596561914…45694413797464473601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

4.911 × 10⁹⁸(99-digit number)

49119734785193123828…91388827594928947201

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 Cunningham Chain of the Second Kind. 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 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 2789393

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 f5c0ecc895fb9397c830ff8362c577dd7399c922f8145151c05336a996fea5e4

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 #2,789,393 on Chainz ↗

Block #2,789,393

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