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Block #322,402

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/20/2013, 11:35:51 PM Β· Difficulty 10.1943 Β· 6,495,599 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e8ca72011d186e0f7531f8d634ec4614c92db7fa10acc93feb41e8d10c77295d
View on Chainz β†—

Height

#322,402

Difficulty

10.194265

Transactions

1

Size

201 B

Version

2

Bits

0a31bb53

Nonce

81,325

Timestamp

12/20/2013, 11:35:51 PM

Confirmations

6,495,599

Merkle Root

cff7793c68ccfaadde128dc86159d6ce4668d65cedc264f2664a27ea93331a6d
Transactions (1)
Coinbasecff7793c68ccfa…4a27ea93331a6d
1 in β†’ 1 out9.6100 XPM110 B
AeKNrjNj…1NEq95Ta
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.

8.187 Γ— 10⁹⁷(98-digit number)
81875026125937039764…17771092298670418550
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
8.187 Γ— 10⁹⁷(98-digit number)
81875026125937039764…17771092298670418549
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.637 Γ— 10⁹⁸(99-digit number)
16375005225187407952…35542184597340837099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.275 Γ— 10⁹⁸(99-digit number)
32750010450374815905…71084369194681674199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.550 Γ— 10⁹⁸(99-digit number)
65500020900749631811…42168738389363348399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.310 Γ— 10⁹⁹(100-digit number)
13100004180149926362…84337476778726696799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.620 Γ— 10⁹⁹(100-digit number)
26200008360299852724…68674953557453393599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.240 Γ— 10⁹⁹(100-digit number)
52400016720599705449…37349907114906787199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.048 Γ— 10¹⁰⁰(101-digit number)
10480003344119941089…74699814229813574399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.096 Γ— 10¹⁰⁰(101-digit number)
20960006688239882179…49399628459627148799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.192 Γ— 10¹⁰⁰(101-digit number)
41920013376479764359…98799256919254297599
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 322402

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 e8ca72011d186e0f7531f8d634ec4614c92db7fa10acc93feb41e8d10c77295d

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 #322,402 on Chainz β†—
Circulating Supply:57,788,072 XPMΒ·at block #6,818,000 Β· updates every 60s
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