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Block #446,245

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/16/2014, 10:26:30 AM Β· Difficulty 10.3617 Β· 6,365,933 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2e482385f1433d1d54fc0476129ebceb18cfde82142ad2cf6ebbc6f3a66ea6e6
View on Chainz β†—

Height

#446,245

Difficulty

10.361744

Transactions

1

Size

254 B

Version

2

Bits

0a5c9b3e

Nonce

257,135

Timestamp

3/16/2014, 10:26:30 AM

Confirmations

6,365,933

Merkle Root

331473dcda5cc62e2c6adfff11e088af9898547c4087a06f9b67f9b07c0bb47f
Transactions (1)
Coinbase331473dcda5cc6…67f9b07c0bb47f
1 in β†’ 3 out9.3000 XPM165 B
AMVf7Jrg…xd5AVR7CALzzzbUz…2Cb4jSDNAJno7LX2…vo4wdWtY
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.

1.147 Γ— 10⁹³(94-digit number)
11475856504143312337…89601302291316580800
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
1.147 Γ— 10⁹³(94-digit number)
11475856504143312337…89601302291316580799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.295 Γ— 10⁹³(94-digit number)
22951713008286624675…79202604582633161599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.590 Γ— 10⁹³(94-digit number)
45903426016573249351…58405209165266323199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.180 Γ— 10⁹³(94-digit number)
91806852033146498702…16810418330532646399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.836 Γ— 10⁹⁴(95-digit number)
18361370406629299740…33620836661065292799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.672 Γ— 10⁹⁴(95-digit number)
36722740813258599481…67241673322130585599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.344 Γ— 10⁹⁴(95-digit number)
73445481626517198962…34483346644261171199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.468 Γ— 10⁹⁡(96-digit number)
14689096325303439792…68966693288522342399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.937 Γ— 10⁹⁡(96-digit number)
29378192650606879584…37933386577044684799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.875 Γ— 10⁹⁡(96-digit number)
58756385301213759169…75866773154089369599
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 446245

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 2e482385f1433d1d54fc0476129ebceb18cfde82142ad2cf6ebbc6f3a66ea6e6

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 #446,245 on Chainz β†—
Circulating Supply:57,741,444 XPMΒ·at block #6,812,177 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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