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Home/Chain Registry/Block #2,207,643

Block #2,207,643

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2017, 9:39:15 AM Β· Difficulty 10.9454 Β· 4,635,201 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9d2954c9303ecfdac78caf9d986646db4b85bcb994d6669341e30bbb28582acf
View on Chainz β†—

Difficulty

10.945352

Transactions

1

Size

201 B

Version

2

Bits

0af20293

Nonce

210,838,950

Timestamp

7/15/2017, 9:39:15 AM

Confirmations

4,635,201

Merkle Root

21152c77baf047cf601f7fbeeae92bc7c651482b23895afa5f7f5121abe61ee0
Transactions (1)
Coinbase21152c77baf047…7f5121abe61ee0
1 in β†’ 1 out8.3300 XPM110 B
AN7ttpuY…eTEa5syw
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.

1.742 Γ— 10⁹⁢(97-digit number)
17423683171063241531…65639406771325552640
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
1.742 Γ— 10⁹⁢(97-digit number)
17423683171063241531…65639406771325552641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.484 Γ— 10⁹⁢(97-digit number)
34847366342126483063…31278813542651105281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.969 Γ— 10⁹⁢(97-digit number)
69694732684252966127…62557627085302210561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.393 Γ— 10⁹⁷(98-digit number)
13938946536850593225…25115254170604421121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.787 Γ— 10⁹⁷(98-digit number)
27877893073701186451…50230508341208842241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.575 Γ— 10⁹⁷(98-digit number)
55755786147402372902…00461016682417684481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.115 Γ— 10⁹⁸(99-digit number)
11151157229480474580…00922033364835368961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.230 Γ— 10⁹⁸(99-digit number)
22302314458960949160…01844066729670737921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.460 Γ— 10⁹⁸(99-digit number)
44604628917921898321…03688133459341475841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.920 Γ— 10⁹⁸(99-digit number)
89209257835843796643…07376266918682951681
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 2207643

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 9d2954c9303ecfdac78caf9d986646db4b85bcb994d6669341e30bbb28582acf

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 #2,207,643 on Chainz β†—
Circulating Supply:57,987,097 XPMΒ·at block #6,842,843 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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