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Home/Chain Registry/Block #2,815,524

Block #2,815,524

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/29/2018, 4:19:49 PM Β· Difficulty 11.6834 Β· 4,021,297 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d79d824e9d242773e37d0876085230720472f4e49331adc3f997ca5f4a82d277
View on Chainz β†—

Difficulty

11.683408

Transactions

1

Size

199 B

Version

2

Bits

0baef3d8

Nonce

2,097,426,627

Timestamp

8/29/2018, 4:19:49 PM

Confirmations

4,021,297

Merkle Root

bd670a4cf14174aa28a2d390e8d7a79c0b2e5da56827787dc58a295f3d991bd1
Transactions (1)
Coinbasebd670a4cf14174…8a295f3d991bd1
1 in β†’ 1 out7.3100 XPM109 B
ALQGpaT6…9dLVU1B9
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.

1.387 Γ— 10⁹⁡(96-digit number)
13878439895447752942…84735969794599175680
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.387 Γ— 10⁹⁡(96-digit number)
13878439895447752942…84735969794599175679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.775 Γ— 10⁹⁡(96-digit number)
27756879790895505885…69471939589198351359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.551 Γ— 10⁹⁡(96-digit number)
55513759581791011770…38943879178396702719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.110 Γ— 10⁹⁢(97-digit number)
11102751916358202354…77887758356793405439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.220 Γ— 10⁹⁢(97-digit number)
22205503832716404708…55775516713586810879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.441 Γ— 10⁹⁢(97-digit number)
44411007665432809416…11551033427173621759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.882 Γ— 10⁹⁢(97-digit number)
88822015330865618833…23102066854347243519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.776 Γ— 10⁹⁷(98-digit number)
17764403066173123766…46204133708694487039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.552 Γ— 10⁹⁷(98-digit number)
35528806132346247533…92408267417388974079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.105 Γ— 10⁹⁷(98-digit number)
71057612264692495066…84816534834777948159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.421 Γ— 10⁹⁸(99-digit number)
14211522452938499013…69633069669555896319
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2815524

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 d79d824e9d242773e37d0876085230720472f4e49331adc3f997ca5f4a82d277

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 #2,815,524 on Chainz β†—
Circulating Supply:57,938,853 XPMΒ·at block #6,836,820 Β· updates every 60s
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