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Block #452,050

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/20/2014, 8:30:50 AM Β· Difficulty 10.3847 Β· 6,373,606 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4ef0864272381cf10cdfee6a98da894412474c8cec268d22c0147ca8b37cfa5b
View on Chainz β†—

Height

#452,050

Difficulty

10.384684

Transactions

1

Size

207 B

Version

2

Bits

0a627aab

Nonce

307,092

Timestamp

3/20/2014, 8:30:50 AM

Confirmations

6,373,606

Merkle Root

fc4bb568b2527cdb06bd929c66a4cf67fad0864aa8c38ce128600e9695686ac0
Transactions (1)
Coinbasefc4bb568b2527c…600e9695686ac0
1 in β†’ 1 out9.2600 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.

1.054 Γ— 10⁹⁸(99-digit number)
10544122590506696342…73419529457479907600
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
1.054 Γ— 10⁹⁸(99-digit number)
10544122590506696342…73419529457479907599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.108 Γ— 10⁹⁸(99-digit number)
21088245181013392685…46839058914959815199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.217 Γ— 10⁹⁸(99-digit number)
42176490362026785371…93678117829919630399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.435 Γ— 10⁹⁸(99-digit number)
84352980724053570742…87356235659839260799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.687 Γ— 10⁹⁹(100-digit number)
16870596144810714148…74712471319678521599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.374 Γ— 10⁹⁹(100-digit number)
33741192289621428296…49424942639357043199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.748 Γ— 10⁹⁹(100-digit number)
67482384579242856593…98849885278714086399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.349 Γ— 10¹⁰⁰(101-digit number)
13496476915848571318…97699770557428172799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.699 Γ— 10¹⁰⁰(101-digit number)
26992953831697142637…95399541114856345599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.398 Γ— 10¹⁰⁰(101-digit number)
53985907663394285275…90799082229712691199
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 452050

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 4ef0864272381cf10cdfee6a98da894412474c8cec268d22c0147ca8b37cfa5b

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 #452,050 on Chainz β†—
Circulating Supply:57,849,354 XPMΒ·at block #6,825,655 Β· updates every 60s
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