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Block #452,518

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/20/2014, 3:30:56 PM Β· Difficulty 10.3907 Β· 6,374,486 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3d92bf8d40e1abf6b334fc62578b483435082e17d0d06dc4b0a6213811daa46c
View on Chainz β†—

Height

#452,518

Difficulty

10.390658

Transactions

1

Size

199 B

Version

2

Bits

0a640229

Nonce

1,164,672,636

Timestamp

3/20/2014, 3:30:56 PM

Confirmations

6,374,486

Merkle Root

43557cfcc4edbf134960c539413478b14d1803fdff75826beb3ebe9358fe081e
Transactions (1)
Coinbase43557cfcc4edbf…3ebe9358fe081e
1 in β†’ 1 out9.2500 XPM109 B
AZvwgkbJ…oNudBGL5
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.

3.951 Γ— 10⁹³(94-digit number)
39512276203584079148…08696487766186558950
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
3.951 Γ— 10⁹³(94-digit number)
39512276203584079148…08696487766186558949
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.902 Γ— 10⁹³(94-digit number)
79024552407168158297…17392975532373117899
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.580 Γ— 10⁹⁴(95-digit number)
15804910481433631659…34785951064746235799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.160 Γ— 10⁹⁴(95-digit number)
31609820962867263319…69571902129492471599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.321 Γ— 10⁹⁴(95-digit number)
63219641925734526638…39143804258984943199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.264 Γ— 10⁹⁡(96-digit number)
12643928385146905327…78287608517969886399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.528 Γ— 10⁹⁡(96-digit number)
25287856770293810655…56575217035939772799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.057 Γ— 10⁹⁡(96-digit number)
50575713540587621310…13150434071879545599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.011 Γ— 10⁹⁢(97-digit number)
10115142708117524262…26300868143759091199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.023 Γ— 10⁹⁢(97-digit number)
20230285416235048524…52601736287518182399
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 452518

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 3d92bf8d40e1abf6b334fc62578b483435082e17d0d06dc4b0a6213811daa46c

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 #452,518 on Chainz β†—
Circulating Supply:57,860,208 XPMΒ·at block #6,827,003 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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