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Block #888,040

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/9/2015, 6:10:20 AM Β· Difficulty 10.9559 Β· 5,938,705 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4c60cec2075a3a4eacad84a23a2bdad532499afe6a3bf7ac8774fd326521b5b5
View on Chainz β†—

Height

#888,040

Difficulty

10.955871

Transactions

1

Size

206 B

Version

2

Bits

0af4b3f2

Nonce

6,622,017

Timestamp

1/9/2015, 6:10:20 AM

Confirmations

5,938,705

Merkle Root

2c918845245340b9adb05d2b61ae9e1f7334dd0da5a2dc9abe777182a50b8030
Transactions (1)
Coinbase2c918845245340…777182a50b8030
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.120 Γ— 10⁹⁡(96-digit number)
11207409301111448138…68124289560434975080
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
1.120 Γ— 10⁹⁡(96-digit number)
11207409301111448138…68124289560434975079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.241 Γ— 10⁹⁡(96-digit number)
22414818602222896277…36248579120869950159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.482 Γ— 10⁹⁡(96-digit number)
44829637204445792555…72497158241739900319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.965 Γ— 10⁹⁡(96-digit number)
89659274408891585110…44994316483479800639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.793 Γ— 10⁹⁢(97-digit number)
17931854881778317022…89988632966959601279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.586 Γ— 10⁹⁢(97-digit number)
35863709763556634044…79977265933919202559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.172 Γ— 10⁹⁢(97-digit number)
71727419527113268088…59954531867838405119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.434 Γ— 10⁹⁷(98-digit number)
14345483905422653617…19909063735676810239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.869 Γ— 10⁹⁷(98-digit number)
28690967810845307235…39818127471353620479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.738 Γ— 10⁹⁷(98-digit number)
57381935621690614470…79636254942707240959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.147 Γ— 10⁹⁸(99-digit number)
11476387124338122894…59272509885414481919
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 888040

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 4c60cec2075a3a4eacad84a23a2bdad532499afe6a3bf7ac8774fd326521b5b5

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 #888,040 on Chainz β†—
Circulating Supply:57,858,117 XPMΒ·at block #6,826,744 Β· updates every 60s
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