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Block #572,002

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/1/2014, 7:55:47 PM Β· Difficulty 10.9658 Β· 6,243,886 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c1214fddff774394e37a3dbd5bbb06ec450bce7e02be1612c320e9ff4aac986f
View on Chainz β†—

Height

#572,002

Difficulty

10.965807

Transactions

1

Size

208 B

Version

2

Bits

0af73f28

Nonce

2,460,061,710

Timestamp

6/1/2014, 7:55:47 PM

Confirmations

6,243,886

Merkle Root

eb8a8148be65d4eef0a3495bd9c55db5b503bf4c359162e166435ad4ead6c79a
Transactions (1)
Coinbaseeb8a8148be65d4…435ad4ead6c79a
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.161 Γ— 10⁹⁹(100-digit number)
11610515464567891561…61450723319515985920
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.161 Γ— 10⁹⁹(100-digit number)
11610515464567891561…61450723319515985921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.322 Γ— 10⁹⁹(100-digit number)
23221030929135783123…22901446639031971841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.644 Γ— 10⁹⁹(100-digit number)
46442061858271566246…45802893278063943681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.288 Γ— 10⁹⁹(100-digit number)
92884123716543132493…91605786556127887361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.857 Γ— 10¹⁰⁰(101-digit number)
18576824743308626498…83211573112255774721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.715 Γ— 10¹⁰⁰(101-digit number)
37153649486617252997…66423146224511549441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.430 Γ— 10¹⁰⁰(101-digit number)
74307298973234505994…32846292449023098881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.486 Γ— 10¹⁰¹(102-digit number)
14861459794646901198…65692584898046197761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.972 Γ— 10¹⁰¹(102-digit number)
29722919589293802397…31385169796092395521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.944 Γ— 10¹⁰¹(102-digit number)
59445839178587604795…62770339592184791041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.188 Γ— 10¹⁰²(103-digit number)
11889167835717520959…25540679184369582081
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 572002

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 c1214fddff774394e37a3dbd5bbb06ec450bce7e02be1612c320e9ff4aac986f

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 #572,002 on Chainz β†—
Circulating Supply:57,771,218 XPMΒ·at block #6,815,887 Β· updates every 60s
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