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Block #576,570

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/4/2014, 4:46:29 PM Β· Difficulty 10.9688 Β· 6,250,400 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8fcd82a3aa17cfab5e37b25084b6f4540b72ecbbb0bd76f3faa75e1b700c0518
View on Chainz β†—

Height

#576,570

Difficulty

10.968786

Transactions

3

Size

658 B

Version

2

Bits

0af8025e

Nonce

765,161,366

Timestamp

6/4/2014, 4:46:29 PM

Confirmations

6,250,400

Merkle Root

1f2396bb3d79d75ca7d296f1c6e0df51d79a068bc05a57e2a4c11df9e3ff78a5
Transactions (3)
Coinbase8224cbada58334…e038c186bbe49b
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
1a0cda35ef72de…944e54922b4b4c
1 in β†’ 2 out7.7336 XPM226 B
AKCd69dJ…8BiqsTaHAVgL31FS…MM5ddUzx
3405f1da556924…52c3199d3adec1
1 in β†’ 2 out7.5945 XPM225 B
AS9ZCvju…bu3NEFwZAGNcAtJk…b7amGzKH
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.

6.458 Γ— 10⁹⁢(97-digit number)
64582025855031959188…01941426209944250480
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
6.458 Γ— 10⁹⁢(97-digit number)
64582025855031959188…01941426209944250481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.291 Γ— 10⁹⁷(98-digit number)
12916405171006391837…03882852419888500961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.583 Γ— 10⁹⁷(98-digit number)
25832810342012783675…07765704839777001921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.166 Γ— 10⁹⁷(98-digit number)
51665620684025567350…15531409679554003841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.033 Γ— 10⁹⁸(99-digit number)
10333124136805113470…31062819359108007681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.066 Γ— 10⁹⁸(99-digit number)
20666248273610226940…62125638718216015361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.133 Γ— 10⁹⁸(99-digit number)
41332496547220453880…24251277436432030721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.266 Γ— 10⁹⁸(99-digit number)
82664993094440907760…48502554872864061441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.653 Γ— 10⁹⁹(100-digit number)
16532998618888181552…97005109745728122881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.306 Γ— 10⁹⁹(100-digit number)
33065997237776363104…94010219491456245761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.613 Γ— 10⁹⁹(100-digit number)
66131994475552726208…88020438982912491521
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 576570

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 8fcd82a3aa17cfab5e37b25084b6f4540b72ecbbb0bd76f3faa75e1b700c0518

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 #576,570 on Chainz β†—
Circulating Supply:57,859,934 XPMΒ·at block #6,826,969 Β· updates every 60s
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