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Block #843,223

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/7/2014, 6:03:52 AM Β· Difficulty 10.9732 Β· 6,001,866 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8d373e3cd028f9ed8b1bcbd141e0c790ca427698b25097803000552e5c0658e8
View on Chainz β†—

Height

#843,223

Difficulty

10.973178

Transactions

2

Size

434 B

Version

2

Bits

0af92231

Nonce

377,818,632

Timestamp

12/7/2014, 6:03:52 AM

Confirmations

6,001,866

Merkle Root

d587dac731ca61ad8fa7f205bc573ace825b049def43d4ee79b17871b1777394
Transactions (2)
Coinbasefc451083be8273…232ccba71e9a47
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
a69afe1e7bfdb3…1ac85c5c5181ed
1 in β†’ 2 out0.8801 XPM227 B
AdaWA6w9…oMNAqabHANfxFZLt…P1KRxBRh
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.

2.211 Γ— 10⁹⁢(97-digit number)
22112759833325786207…77059491783322531200
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
2.211 Γ— 10⁹⁢(97-digit number)
22112759833325786207…77059491783322531199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.422 Γ— 10⁹⁢(97-digit number)
44225519666651572415…54118983566645062399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.845 Γ— 10⁹⁢(97-digit number)
88451039333303144830…08237967133290124799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.769 Γ— 10⁹⁷(98-digit number)
17690207866660628966…16475934266580249599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.538 Γ— 10⁹⁷(98-digit number)
35380415733321257932…32951868533160499199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.076 Γ— 10⁹⁷(98-digit number)
70760831466642515864…65903737066320998399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.415 Γ— 10⁹⁸(99-digit number)
14152166293328503172…31807474132641996799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.830 Γ— 10⁹⁸(99-digit number)
28304332586657006345…63614948265283993599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.660 Γ— 10⁹⁸(99-digit number)
56608665173314012691…27229896530567987199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.132 Γ— 10⁹⁹(100-digit number)
11321733034662802538…54459793061135974399
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 843223

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 8d373e3cd028f9ed8b1bcbd141e0c790ca427698b25097803000552e5c0658e8

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 #843,223 on Chainz β†—
Circulating Supply:58,005,140 XPMΒ·at block #6,845,088 Β· updates every 60s
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