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Home/Chain Registry/Block #3,569,561

Block #3,569,561

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/23/2020, 8:27:06 AM Β· Difficulty 10.9051 Β· 3,272,474 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
33a1ba3bc25daca54b51f1f8f478032d45df864bd206ee78209d1571a0911458
View on Chainz β†—

Difficulty

10.905073

Transactions

1

Size

199 B

Version

2

Bits

0ae7b2e4

Nonce

1,527,758,394

Timestamp

2/23/2020, 8:27:06 AM

Confirmations

3,272,474

Merkle Root

68579929937093ac5e103ba22251fa4b1d5ecbcc755b979ff3e730bea279a73e
Transactions (1)
Coinbase68579929937093…e730bea279a73e
1 in β†’ 1 out8.4000 XPM109 B
ASiq2qtK…VMhmk7yL
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.

4.199 Γ— 10⁹⁴(95-digit number)
41994521058200592579…11376620263495360000
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
4.199 Γ— 10⁹⁴(95-digit number)
41994521058200592579…11376620263495360001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.398 Γ— 10⁹⁴(95-digit number)
83989042116401185159…22753240526990720001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.679 Γ— 10⁹⁡(96-digit number)
16797808423280237031…45506481053981440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.359 Γ— 10⁹⁡(96-digit number)
33595616846560474063…91012962107962880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.719 Γ— 10⁹⁡(96-digit number)
67191233693120948127…82025924215925760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.343 Γ— 10⁹⁢(97-digit number)
13438246738624189625…64051848431851520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.687 Γ— 10⁹⁢(97-digit number)
26876493477248379250…28103696863703040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.375 Γ— 10⁹⁢(97-digit number)
53752986954496758501…56207393727406080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.075 Γ— 10⁹⁷(98-digit number)
10750597390899351700…12414787454812160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.150 Γ— 10⁹⁷(98-digit number)
21501194781798703400…24829574909624320001
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 3569561

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 33a1ba3bc25daca54b51f1f8f478032d45df864bd206ee78209d1571a0911458

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 #3,569,561 on Chainz β†—
Circulating Supply:57,980,668 XPMΒ·at block #6,842,034 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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