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Block #218,801

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/20/2013, 3:32:58 AM Β· Difficulty 9.9313 Β· 6,608,198 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fc7da72429c9f2c108d57b7b5faeb7ef51d4719b81a621ca57eb1977dd3c3c41
View on Chainz β†—

Height

#218,801

Difficulty

9.931348

Transactions

1

Size

200 B

Version

2

Bits

09ee6ccc

Nonce

183,889

Timestamp

10/20/2013, 3:32:58 AM

Confirmations

6,608,198

Merkle Root

28ee900b6476228594ef1b4881206cccf65c9a82b942cd165c46fa0f9529212b
Transactions (1)
Coinbase28ee900b647622…46fa0f9529212b
1 in β†’ 1 out10.1200 XPM110 B
AbuU1HhS…JPwsJEbB
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.

3.856 Γ— 10⁹⁡(96-digit number)
38566117483222691705…49402423909950753280
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
3.856 Γ— 10⁹⁡(96-digit number)
38566117483222691705…49402423909950753279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.713 Γ— 10⁹⁡(96-digit number)
77132234966445383410…98804847819901506559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.542 Γ— 10⁹⁢(97-digit number)
15426446993289076682…97609695639803013119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.085 Γ— 10⁹⁢(97-digit number)
30852893986578153364…95219391279606026239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.170 Γ— 10⁹⁢(97-digit number)
61705787973156306728…90438782559212052479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.234 Γ— 10⁹⁷(98-digit number)
12341157594631261345…80877565118424104959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.468 Γ— 10⁹⁷(98-digit number)
24682315189262522691…61755130236848209919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.936 Γ— 10⁹⁷(98-digit number)
49364630378525045382…23510260473696419839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.872 Γ— 10⁹⁷(98-digit number)
98729260757050090765…47020520947392839679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.974 Γ— 10⁹⁸(99-digit number)
19745852151410018153…94041041894785679359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 218801

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 fc7da72429c9f2c108d57b7b5faeb7ef51d4719b81a621ca57eb1977dd3c3c41

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 #218,801 on Chainz β†—
Circulating Supply:57,860,168 XPMΒ·at block #6,826,998 Β· updates every 60s
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