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Home/Chain Registry/Block #533,581

Block #533,581

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/9/2014, 7:16:00 PM Β· Difficulty 10.9000 Β· 6,280,291 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9761af3d07a2e44166b493f5765bcc4372bbf2a7ca6d1a153d24c276bc4a350e
View on Chainz β†—

Height

#533,581

Difficulty

10.900046

Transactions

2

Size

398 B

Version

2

Bits

0ae66969

Nonce

59,567,008

Timestamp

5/9/2014, 7:16:00 PM

Confirmations

6,280,291

Merkle Root

4253bbbbe5382c680199b75e6f4396eb93a279bc9a2ffdf92adb2afa6495058e
Transactions (2)
Coinbased625cf87929843…a078c488694b86
1 in β†’ 1 out8.4100 XPM116 B
ANSXnLY2…Sd25TjkD
ab39501c30c62c…97ea965c25d629
1 in β†’ 2 out8.4100 XPM191 B
AeKNrjNj…1NEq95TaAc5Sc2Mv…q4gm41o8
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.

1.287 Γ— 10⁹⁸(99-digit number)
12873668282135918478…17256751148487201800
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
1.287 Γ— 10⁹⁸(99-digit number)
12873668282135918478…17256751148487201799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.574 Γ— 10⁹⁸(99-digit number)
25747336564271836956…34513502296974403599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.149 Γ— 10⁹⁸(99-digit number)
51494673128543673912…69027004593948807199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.029 Γ— 10⁹⁹(100-digit number)
10298934625708734782…38054009187897614399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.059 Γ— 10⁹⁹(100-digit number)
20597869251417469564…76108018375795228799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.119 Γ— 10⁹⁹(100-digit number)
41195738502834939129…52216036751590457599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.239 Γ— 10⁹⁹(100-digit number)
82391477005669878259…04432073503180915199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.647 Γ— 10¹⁰⁰(101-digit number)
16478295401133975651…08864147006361830399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.295 Γ— 10¹⁰⁰(101-digit number)
32956590802267951303…17728294012723660799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.591 Γ— 10¹⁰⁰(101-digit number)
65913181604535902607…35456588025447321599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.318 Γ— 10¹⁰¹(102-digit number)
13182636320907180521…70913176050894643199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 533581

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 9761af3d07a2e44166b493f5765bcc4372bbf2a7ca6d1a153d24c276bc4a350e

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 #533,581 on Chainz β†—
Circulating Supply:57,755,050 XPMΒ·at block #6,813,871 Β· updates every 60s
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