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Block #283,419

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/29/2013, 5:42:03 PM Β· Difficulty 9.9812 Β· 6,541,559 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4f9f1fdf4f5938855fb363af727e72bcde4a6162cef63afacaf157dbd0dbe1a5
View on Chainz β†—

Height

#283,419

Difficulty

9.981165

Transactions

1

Size

206 B

Version

2

Bits

09fb2d9b

Nonce

218,979

Timestamp

11/29/2013, 5:42:03 PM

Confirmations

6,541,559

Merkle Root

c9aa2e2c6a69ebbbaa3224fcdd36cb4400c3a10ad1c92850e0199f6f3d6eef7c
Transactions (1)
Coinbasec9aa2e2c6a69eb…199f6f3d6eef7c
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.

3.067 Γ— 10⁹⁴(95-digit number)
30677142735282921535…32349475435669072280
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
3.067 Γ— 10⁹⁴(95-digit number)
30677142735282921535…32349475435669072279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.135 Γ— 10⁹⁴(95-digit number)
61354285470565843070…64698950871338144559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.227 Γ— 10⁹⁡(96-digit number)
12270857094113168614…29397901742676289119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.454 Γ— 10⁹⁡(96-digit number)
24541714188226337228…58795803485352578239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.908 Γ— 10⁹⁡(96-digit number)
49083428376452674456…17591606970705156479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.816 Γ— 10⁹⁡(96-digit number)
98166856752905348913…35183213941410312959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.963 Γ— 10⁹⁢(97-digit number)
19633371350581069782…70366427882820625919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.926 Γ— 10⁹⁢(97-digit number)
39266742701162139565…40732855765641251839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.853 Γ— 10⁹⁢(97-digit number)
78533485402324279130…81465711531282503679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.570 Γ— 10⁹⁷(98-digit number)
15706697080464855826…62931423062565007359
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 283419

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 4f9f1fdf4f5938855fb363af727e72bcde4a6162cef63afacaf157dbd0dbe1a5

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 #283,419 on Chainz β†—
Circulating Supply:57,843,905 XPMΒ·at block #6,824,977 Β· updates every 60s
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