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Block #284,434

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/30/2013, 3:13:55 AM Β· Difficulty 9.9827 Β· 6,532,500 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9f8e7aa026143484632fd3d0b0a86e5fda1c5eb17ab8754e819b265de5a791e9
View on Chainz β†—

Height

#284,434

Difficulty

9.982704

Transactions

1

Size

211 B

Version

2

Bits

09fb9279

Nonce

1,679

Timestamp

11/30/2013, 3:13:55 AM

Confirmations

6,532,500

Merkle Root

7e0fbf4542932bca5f4ee2ac2130eb81a42222205ff3294d9a1854c46b1351ec
Transactions (1)
Coinbase7e0fbf4542932b…1854c46b1351ec
1 in β†’ 1 out10.0200 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.

7.568 Γ— 10¹⁰⁡(106-digit number)
75685028750687356007…36641697267764428800
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
7.568 Γ— 10¹⁰⁡(106-digit number)
75685028750687356007…36641697267764428799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.513 Γ— 10¹⁰⁢(107-digit number)
15137005750137471201…73283394535528857599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.027 Γ— 10¹⁰⁢(107-digit number)
30274011500274942402…46566789071057715199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.054 Γ— 10¹⁰⁢(107-digit number)
60548023000549884805…93133578142115430399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.210 Γ— 10¹⁰⁷(108-digit number)
12109604600109976961…86267156284230860799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.421 Γ— 10¹⁰⁷(108-digit number)
24219209200219953922…72534312568461721599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.843 Γ— 10¹⁰⁷(108-digit number)
48438418400439907844…45068625136923443199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.687 Γ— 10¹⁰⁷(108-digit number)
96876836800879815689…90137250273846886399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.937 Γ— 10¹⁰⁸(109-digit number)
19375367360175963137…80274500547693772799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.875 Γ— 10¹⁰⁸(109-digit number)
38750734720351926275…60549001095387545599
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 284434

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 9f8e7aa026143484632fd3d0b0a86e5fda1c5eb17ab8754e819b265de5a791e9

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 #284,434 on Chainz β†—
Circulating Supply:57,779,514 XPMΒ·at block #6,816,933 Β· updates every 60s
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