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Home/Chain Registry/Block #82,844

Block #82,844

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/25/2013, 5:20:44 PM Β· Difficulty 9.2735 Β· 6,714,749 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3341a2c9b58c7fb2166688b829f65ab5ab8e2952523de0ef6c219b15a9d9dd5a
View on Chainz β†—

Height

#82,844

Difficulty

9.273477

Transactions

1

Size

204 B

Version

2

Bits

09460298

Nonce

82,914

Timestamp

7/25/2013, 5:20:44 PM

Confirmations

6,714,749

Merkle Root

d2c59a881d8ea64d43103690f9222983c375e37145810f690c0f85cbcaa56920
Transactions (1)
Coinbased2c59a881d8ea6…0f85cbcaa56920
1 in β†’ 1 out11.6100 XPM109 B
AQZnEJLb…LtrLu6Go
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.

1.851 Γ— 10¹⁰⁢(107-digit number)
18516566382379045449…97902737878990454120
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
1.851 Γ— 10¹⁰⁢(107-digit number)
18516566382379045449…97902737878990454119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.703 Γ— 10¹⁰⁢(107-digit number)
37033132764758090898…95805475757980908239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.406 Γ— 10¹⁰⁢(107-digit number)
74066265529516181796…91610951515961816479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.481 Γ— 10¹⁰⁷(108-digit number)
14813253105903236359…83221903031923632959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.962 Γ— 10¹⁰⁷(108-digit number)
29626506211806472718…66443806063847265919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.925 Γ— 10¹⁰⁷(108-digit number)
59253012423612945437…32887612127694531839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.185 Γ— 10¹⁰⁸(109-digit number)
11850602484722589087…65775224255389063679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.370 Γ— 10¹⁰⁸(109-digit number)
23701204969445178174…31550448510778127359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.740 Γ— 10¹⁰⁸(109-digit number)
47402409938890356349…63100897021556254719
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 82844

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 3341a2c9b58c7fb2166688b829f65ab5ab8e2952523de0ef6c219b15a9d9dd5a

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 #82,844 on Chainz β†—
Circulating Supply:57,624,725 XPMΒ·at block #6,797,592 Β· updates every 60s
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