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Block #321,318

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/20/2013, 5:55:12 AM Β· Difficulty 10.1902 Β· 6,491,127 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
87519882cacc9e7efdb67c53eb131cecf0aad0ed436b5eccdb2739fc05c14c44
View on Chainz β†—

Height

#321,318

Difficulty

10.190168

Transactions

1

Size

204 B

Version

2

Bits

0a30aed2

Nonce

155,972

Timestamp

12/20/2013, 5:55:12 AM

Confirmations

6,491,127

Merkle Root

2d6acfc18ebf548146063e11943a22f00511c8aeeed500f2fbad0e35877ee2d5
Transactions (1)
Coinbase2d6acfc18ebf54…ad0e35877ee2d5
1 in β†’ 1 out9.6200 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.

1.068 Γ— 10¹⁰⁴(105-digit number)
10687140053489708668…65268525822674530840
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
1.068 Γ— 10¹⁰⁴(105-digit number)
10687140053489708668…65268525822674530841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.137 Γ— 10¹⁰⁴(105-digit number)
21374280106979417337…30537051645349061681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.274 Γ— 10¹⁰⁴(105-digit number)
42748560213958834674…61074103290698123361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.549 Γ— 10¹⁰⁴(105-digit number)
85497120427917669348…22148206581396246721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.709 Γ— 10¹⁰⁡(106-digit number)
17099424085583533869…44296413162792493441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.419 Γ— 10¹⁰⁡(106-digit number)
34198848171167067739…88592826325584986881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.839 Γ— 10¹⁰⁡(106-digit number)
68397696342334135478…77185652651169973761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.367 Γ— 10¹⁰⁢(107-digit number)
13679539268466827095…54371305302339947521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.735 Γ— 10¹⁰⁢(107-digit number)
27359078536933654191…08742610604679895041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.471 Γ— 10¹⁰⁢(107-digit number)
54718157073867308382…17485221209359790081
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 321318

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 87519882cacc9e7efdb67c53eb131cecf0aad0ed436b5eccdb2739fc05c14c44

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 #321,318 on Chainz β†—
Circulating Supply:57,743,583 XPMΒ·at block #6,812,444 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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