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Home/Chain Registry/Block #569,448

Block #569,448

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/31/2014, 4:08:36 AM Β· Difficulty 10.9646 Β· 6,230,549 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2cee66f793ea448765afe7c5996b76934ded7bc27a445c0830c91c0b2fbaedc7
View on Chainz β†—

Height

#569,448

Difficulty

10.964573

Transactions

1

Size

208 B

Version

2

Bits

0af6ee3e

Nonce

257,532,598

Timestamp

5/31/2014, 4:08:36 AM

Confirmations

6,230,549

Merkle Root

e21ef9e2155887aeeed83a229aaa3aa9f4396f520397508d5dff1c1d460f7585
Transactions (1)
Coinbasee21ef9e2155887…ff1c1d460f7585
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.

6.297 Γ— 10⁹⁹(100-digit number)
62977913101236085233…44678970948644700160
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
6.297 Γ— 10⁹⁹(100-digit number)
62977913101236085233…44678970948644700161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.259 Γ— 10¹⁰⁰(101-digit number)
12595582620247217046…89357941897289400321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.519 Γ— 10¹⁰⁰(101-digit number)
25191165240494434093…78715883794578800641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.038 Γ— 10¹⁰⁰(101-digit number)
50382330480988868186…57431767589157601281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.007 Γ— 10¹⁰¹(102-digit number)
10076466096197773637…14863535178315202561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.015 Γ— 10¹⁰¹(102-digit number)
20152932192395547274…29727070356630405121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.030 Γ— 10¹⁰¹(102-digit number)
40305864384791094549…59454140713260810241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.061 Γ— 10¹⁰¹(102-digit number)
80611728769582189099…18908281426521620481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.612 Γ— 10¹⁰²(103-digit number)
16122345753916437819…37816562853043240961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.224 Γ— 10¹⁰²(103-digit number)
32244691507832875639…75633125706086481921
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 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
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 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 569448

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 2cee66f793ea448765afe7c5996b76934ded7bc27a445c0830c91c0b2fbaedc7

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 #569,448 on Chainz β†—
Circulating Supply:57,644,039 XPMΒ·at block #6,799,996 Β· updates every 60s
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