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Block #282,567

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/29/2013, 10:38:09 AM Β· Difficulty 9.9794 Β· 6,542,324 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
73f457528e4990202722efe1cc0f2bd944735e219155421002ab97800b53f1b1
View on Chainz β†—

Height

#282,567

Difficulty

9.979375

Transactions

1

Size

210 B

Version

2

Bits

09fab854

Nonce

1,230

Timestamp

11/29/2013, 10:38:09 AM

Confirmations

6,542,324

Merkle Root

084c0a6d0a05787a375636879a993e0dd57d77371df056421739ba4fde2afe5f
Transactions (1)
Coinbase084c0a6d0a0578…39ba4fde2afe5f
1 in β†’ 1 out10.0300 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.622 Γ— 10¹⁰⁡(106-digit number)
16223944860367587270…30150582456816762880
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
1.622 Γ— 10¹⁰⁡(106-digit number)
16223944860367587270…30150582456816762879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.244 Γ— 10¹⁰⁡(106-digit number)
32447889720735174540…60301164913633525759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.489 Γ— 10¹⁰⁡(106-digit number)
64895779441470349081…20602329827267051519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.297 Γ— 10¹⁰⁢(107-digit number)
12979155888294069816…41204659654534103039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.595 Γ— 10¹⁰⁢(107-digit number)
25958311776588139632…82409319309068206079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.191 Γ— 10¹⁰⁢(107-digit number)
51916623553176279265…64818638618136412159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.038 Γ— 10¹⁰⁷(108-digit number)
10383324710635255853…29637277236272824319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.076 Γ— 10¹⁰⁷(108-digit number)
20766649421270511706…59274554472545648639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.153 Γ— 10¹⁰⁷(108-digit number)
41533298842541023412…18549108945091297279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.306 Γ— 10¹⁰⁷(108-digit number)
83066597685082046824…37098217890182594559
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 282567

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 73f457528e4990202722efe1cc0f2bd944735e219155421002ab97800b53f1b1

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 #282,567 on Chainz β†—
Circulating Supply:57,843,209 XPMΒ·at block #6,824,890 Β· updates every 60s
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