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Home/Chain Registry/Block #1,187,182

Block #1,187,182

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2015, 8:20:02 PM Β· Difficulty 10.8793 Β· 5,639,476 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
65e4bfde458c1638b79fd4492deee9ceff7220f7c03a5bf8ecbfe635b5dcf82e
View on Chainz β†—

Difficulty

10.879262

Transactions

1

Size

206 B

Version

2

Bits

0ae11757

Nonce

261,825,150

Timestamp

8/8/2015, 8:20:02 PM

Confirmations

5,639,476

Merkle Root

de06d520a9e0b14bc2705902be8769e96a7688c117157da0976885a922ed97f9
Transactions (1)
Coinbasede06d520a9e0b1…6885a922ed97f9
1 in β†’ 1 out8.4400 XPM116 B
AJCEY9yy…tg97E6zm
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.

5.673 Γ— 10⁹⁡(96-digit number)
56732296642760632585…53682444133815236000
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
5.673 Γ— 10⁹⁡(96-digit number)
56732296642760632585…53682444133815235999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.134 Γ— 10⁹⁢(97-digit number)
11346459328552126517…07364888267630471999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.269 Γ— 10⁹⁢(97-digit number)
22692918657104253034…14729776535260943999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.538 Γ— 10⁹⁢(97-digit number)
45385837314208506068…29459553070521887999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.077 Γ— 10⁹⁢(97-digit number)
90771674628417012136…58919106141043775999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.815 Γ— 10⁹⁷(98-digit number)
18154334925683402427…17838212282087551999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.630 Γ— 10⁹⁷(98-digit number)
36308669851366804854…35676424564175103999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.261 Γ— 10⁹⁷(98-digit number)
72617339702733609709…71352849128350207999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.452 Γ— 10⁹⁸(99-digit number)
14523467940546721941…42705698256700415999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.904 Γ— 10⁹⁸(99-digit number)
29046935881093443883…85411396513400831999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.809 Γ— 10⁹⁸(99-digit number)
58093871762186887767…70822793026801663999
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 1187182

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 65e4bfde458c1638b79fd4492deee9ceff7220f7c03a5bf8ecbfe635b5dcf82e

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 #1,187,182 on Chainz β†—
Circulating Supply:57,857,414 XPMΒ·at block #6,826,657 Β· updates every 60s
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