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Block #320,282

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/19/2013, 1:23:35 PM Β· Difficulty 10.1823 Β· 6,507,040 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d7d2fd9452292a553f4d5bb110cfcfb39f7bf62c01d6746efbf88c8851722ddf
View on Chainz β†—

Height

#320,282

Difficulty

10.182264

Transactions

1

Size

206 B

Version

2

Bits

0a2ea8e1

Nonce

251,658,535

Timestamp

12/19/2013, 1:23:35 PM

Confirmations

6,507,040

Merkle Root

b89f351edac56f02dcca4738203106c6b01d23baa6a0be5979484133df77da1d
Transactions (1)
Coinbaseb89f351edac56f…484133df77da1d
1 in β†’ 1 out9.6300 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.

7.020 Γ— 10⁹⁡(96-digit number)
70201257669064779516…73999491092268672000
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
7.020 Γ— 10⁹⁡(96-digit number)
70201257669064779516…73999491092268671999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.404 Γ— 10⁹⁢(97-digit number)
14040251533812955903…47998982184537343999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.808 Γ— 10⁹⁢(97-digit number)
28080503067625911806…95997964369074687999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.616 Γ— 10⁹⁢(97-digit number)
56161006135251823613…91995928738149375999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.123 Γ— 10⁹⁷(98-digit number)
11232201227050364722…83991857476298751999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.246 Γ— 10⁹⁷(98-digit number)
22464402454100729445…67983714952597503999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.492 Γ— 10⁹⁷(98-digit number)
44928804908201458890…35967429905195007999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.985 Γ— 10⁹⁷(98-digit number)
89857609816402917781…71934859810390015999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.797 Γ— 10⁹⁸(99-digit number)
17971521963280583556…43869719620780031999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.594 Γ— 10⁹⁸(99-digit number)
35943043926561167112…87739439241560063999
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 320282

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 d7d2fd9452292a553f4d5bb110cfcfb39f7bf62c01d6746efbf88c8851722ddf

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 #320,282 on Chainz β†—
Circulating Supply:57,862,688 XPMΒ·at block #6,827,321 Β· updates every 60s
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