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Block #864,223

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/23/2014, 1:57:51 AM Β· Difficulty 10.9625 Β· 5,939,748 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b3bac84856384330b6c1055c6d49c4e5c0ecef5a970a91677d769d6ec132e72c
View on Chainz β†—

Height

#864,223

Difficulty

10.962515

Transactions

1

Size

207 B

Version

2

Bits

0af66769

Nonce

1,584,707,107

Timestamp

12/23/2014, 1:57:51 AM

Confirmations

5,939,748

Merkle Root

002d00b447d4c668a10f650ecc9c4a166dc784cfa45c3aaa2c4c4d0ca361ddd7
Transactions (1)
Coinbase002d00b447d4c6…4c4d0ca361ddd7
1 in β†’ 1 out8.3100 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.

1.828 Γ— 10⁹⁢(97-digit number)
18285990987557412370…26177138394782029600
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
1.828 Γ— 10⁹⁢(97-digit number)
18285990987557412370…26177138394782029599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.657 Γ— 10⁹⁢(97-digit number)
36571981975114824740…52354276789564059199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.314 Γ— 10⁹⁢(97-digit number)
73143963950229649481…04708553579128118399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.462 Γ— 10⁹⁷(98-digit number)
14628792790045929896…09417107158256236799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.925 Γ— 10⁹⁷(98-digit number)
29257585580091859792…18834214316512473599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.851 Γ— 10⁹⁷(98-digit number)
58515171160183719585…37668428633024947199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.170 Γ— 10⁹⁸(99-digit number)
11703034232036743917…75336857266049894399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.340 Γ— 10⁹⁸(99-digit number)
23406068464073487834…50673714532099788799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.681 Γ— 10⁹⁸(99-digit number)
46812136928146975668…01347429064199577599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.362 Γ— 10⁹⁸(99-digit number)
93624273856293951336…02694858128399155199
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 864223

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 b3bac84856384330b6c1055c6d49c4e5c0ecef5a970a91677d769d6ec132e72c

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 #864,223 on Chainz β†—
Circulating Supply:57,675,814 XPMΒ·at block #6,803,970 Β· updates every 60s
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