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Block #322,189

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/20/2013, 7:30:25 PM Β· Difficulty 10.1993 Β· 6,495,297 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3143f520c776801be27bb0f7bb58f2b90de8fa2c8b7b080dcb2c24d58eb49190
View on Chainz β†—

Height

#322,189

Difficulty

10.199328

Transactions

1

Size

210 B

Version

2

Bits

0a330722

Nonce

12,124

Timestamp

12/20/2013, 7:30:25 PM

Confirmations

6,495,297

Merkle Root

ff6e027161e3c8af9122894620080c39c41d3cafd765b32c79f52b77d51ee3e4
Transactions (1)
Coinbaseff6e027161e3c8…f52b77d51ee3e4
1 in β†’ 1 out9.6000 XPM116 B
AbwWkWZt…kawDhufa
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.

5.550 Γ— 10¹⁰⁴(105-digit number)
55502907312402630300…92515560594953569360
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
5.550 Γ— 10¹⁰⁴(105-digit number)
55502907312402630300…92515560594953569361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.110 Γ— 10¹⁰⁡(106-digit number)
11100581462480526060…85031121189907138721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.220 Γ— 10¹⁰⁡(106-digit number)
22201162924961052120…70062242379814277441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.440 Γ— 10¹⁰⁡(106-digit number)
44402325849922104240…40124484759628554881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.880 Γ— 10¹⁰⁡(106-digit number)
88804651699844208481…80248969519257109761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.776 Γ— 10¹⁰⁢(107-digit number)
17760930339968841696…60497939038514219521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.552 Γ— 10¹⁰⁢(107-digit number)
35521860679937683392…20995878077028439041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.104 Γ— 10¹⁰⁢(107-digit number)
71043721359875366785…41991756154056878081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.420 Γ— 10¹⁰⁷(108-digit number)
14208744271975073357…83983512308113756161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.841 Γ— 10¹⁰⁷(108-digit number)
28417488543950146714…67967024616227512321
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 322189

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 3143f520c776801be27bb0f7bb58f2b90de8fa2c8b7b080dcb2c24d58eb49190

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 #322,189 on Chainz β†—
Circulating Supply:57,783,942 XPMΒ·at block #6,817,485 Β· updates every 60s
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