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Home/Chain Registry/Block #2,679,347

Block #2,679,347

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/26/2018, 10:51:52 PM Β· Difficulty 11.6934 Β· 4,164,667 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3acd3b33773fd65fa141816472af9d3b5b3bad0019c30886c8d7c61cbe200cd6
View on Chainz β†—

Difficulty

11.693363

Transactions

2

Size

539 B

Version

2

Bits

0bb18042

Nonce

597,055,677

Timestamp

5/26/2018, 10:51:52 PM

Confirmations

4,164,667

Merkle Root

d353c3efb073bcd86b07a4da85a315d422b5b2c7ab99ca1b01f492b28ce0e8ba
Transactions (2)
Coinbase3d2844b2ca90ad…17f3e8133aca40
1 in β†’ 1 out7.3100 XPM110 B
AUEEaxP1…fHBTXgsT
278ceebd77f527…19381340cc3cd2
2 in β†’ 2 out11.8600 XPM340 B
AHZRKKFA…ELvY2MKQAKw999y4…kyrbeYY5
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.465 Γ— 10⁹³(94-digit number)
34658110769913448613…19141152022403462720
Discovered Prime Numbers
p_k = 2^k Γ— 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.

1
origin + 1
3.465 Γ— 10⁹³(94-digit number)
34658110769913448613…19141152022403462721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.931 Γ— 10⁹³(94-digit number)
69316221539826897227…38282304044806925441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.386 Γ— 10⁹⁴(95-digit number)
13863244307965379445…76564608089613850881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.772 Γ— 10⁹⁴(95-digit number)
27726488615930758891…53129216179227701761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.545 Γ— 10⁹⁴(95-digit number)
55452977231861517782…06258432358455403521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.109 Γ— 10⁹⁡(96-digit number)
11090595446372303556…12516864716910807041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.218 Γ— 10⁹⁡(96-digit number)
22181190892744607112…25033729433821614081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.436 Γ— 10⁹⁡(96-digit number)
44362381785489214225…50067458867643228161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.872 Γ— 10⁹⁡(96-digit number)
88724763570978428451…00134917735286456321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.774 Γ— 10⁹⁢(97-digit number)
17744952714195685690…00269835470572912641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.548 Γ— 10⁹⁢(97-digit number)
35489905428391371380…00539670941145825281
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2679347

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 3acd3b33773fd65fa141816472af9d3b5b3bad0019c30886c8d7c61cbe200cd6

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 β†’ Debug Window β†’ 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 #2,679,347 on Chainz β†—
Circulating Supply:57,996,495 XPMΒ·at block #6,844,013 Β· updates every 60s
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