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Block #84,818

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/27/2013, 1:39:22 AM Β· Difficulty 9.2787 Β· 6,710,121 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1f3defe59a55c2dc700390ffd41ea4bbb18693a5365fef7154e5e8d4f7926368
View on Chainz β†—

Height

#84,818

Difficulty

9.278736

Transactions

1

Size

204 B

Version

2

Bits

09475b39

Nonce

148,796

Timestamp

7/27/2013, 1:39:22 AM

Confirmations

6,710,121

Merkle Root

952edaccb051428ffe05c3502f36ed67e478aec6bfee1d67199254b54874517a
Transactions (1)
Coinbase952edaccb05142…9254b54874517a
1 in β†’ 1 out11.6000 XPM109 B
ARrQST2X…v4wJeQZj
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.

1.113 Γ— 10¹⁰⁷(108-digit number)
11138400808463137173…63594349958115933260
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
1.113 Γ— 10¹⁰⁷(108-digit number)
11138400808463137173…63594349958115933259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.227 Γ— 10¹⁰⁷(108-digit number)
22276801616926274347…27188699916231866519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.455 Γ— 10¹⁰⁷(108-digit number)
44553603233852548695…54377399832463733039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.910 Γ— 10¹⁰⁷(108-digit number)
89107206467705097391…08754799664927466079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.782 Γ— 10¹⁰⁸(109-digit number)
17821441293541019478…17509599329854932159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.564 Γ— 10¹⁰⁸(109-digit number)
35642882587082038956…35019198659709864319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.128 Γ— 10¹⁰⁸(109-digit number)
71285765174164077913…70038397319419728639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.425 Γ— 10¹⁰⁹(110-digit number)
14257153034832815582…40076794638839457279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.851 Γ— 10¹⁰⁹(110-digit number)
28514306069665631165…80153589277678914559
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 84818

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 1f3defe59a55c2dc700390ffd41ea4bbb18693a5365fef7154e5e8d4f7926368

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 #84,818 on Chainz β†—
Circulating Supply:57,603,546 XPMΒ·at block #6,794,938 Β· updates every 60s
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