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Home/Chain Registry/Block #2,668,905

Block #2,668,905

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/19/2018, 9:09:30 PM Β· Difficulty 11.6768 Β· 4,168,058 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6599993178b00cab2dbf5ea54a0fae5723eb0131dcbe832c56e87865fee45e73
View on Chainz β†—

Difficulty

11.676826

Transactions

1

Size

201 B

Version

2

Bits

0bad447b

Nonce

938,052,225

Timestamp

5/19/2018, 9:09:30 PM

Confirmations

4,168,058

Merkle Root

19f7576d3ffe6ef2bb98f5ac0b3519784aebfc0c894490d31151a75b069053d6
Transactions (1)
Coinbase19f7576d3ffe6e…51a75b069053d6
1 in β†’ 1 out7.3200 XPM110 B
AQ28A8nL…XJr1AcHE
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.

6.710 Γ— 10⁹⁷(98-digit number)
67108581792121544907…14649367850198323200
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
6.710 Γ— 10⁹⁷(98-digit number)
67108581792121544907…14649367850198323201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.342 Γ— 10⁹⁸(99-digit number)
13421716358424308981…29298735700396646401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.684 Γ— 10⁹⁸(99-digit number)
26843432716848617963…58597471400793292801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.368 Γ— 10⁹⁸(99-digit number)
53686865433697235926…17194942801586585601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.073 Γ— 10⁹⁹(100-digit number)
10737373086739447185…34389885603173171201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.147 Γ— 10⁹⁹(100-digit number)
21474746173478894370…68779771206346342401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.294 Γ— 10⁹⁹(100-digit number)
42949492346957788740…37559542412692684801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.589 Γ— 10⁹⁹(100-digit number)
85898984693915577481…75119084825385369601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.717 Γ— 10¹⁰⁰(101-digit number)
17179796938783115496…50238169650770739201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.435 Γ— 10¹⁰⁰(101-digit number)
34359593877566230992…00476339301541478401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.871 Γ— 10¹⁰⁰(101-digit number)
68719187755132461985…00952678603082956801
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 2668905

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 6599993178b00cab2dbf5ea54a0fae5723eb0131dcbe832c56e87865fee45e73

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 #2,668,905 on Chainz β†—
Circulating Supply:57,940,003 XPMΒ·at block #6,836,962 Β· updates every 60s
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