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Home/Chain Registry/Block #2,866,684

Block #2,866,684

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/4/2018, 9:29:25 AM Β· Difficulty 11.6680 Β· 3,974,430 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d69241cec61a3e4d49d76d08885d443047a87a23a3c3c5afd19e6058daa7f066
View on Chainz β†—

Difficulty

11.668001

Transactions

1

Size

199 B

Version

2

Bits

0bab0219

Nonce

1,329,590,528

Timestamp

10/4/2018, 9:29:25 AM

Confirmations

3,974,430

Merkle Root

0b8b9e1fae34316514c918fb09f471149e845b6d9a2f0c3d41e873deb9d828e8
Transactions (1)
Coinbase0b8b9e1fae3431…e873deb9d828e8
1 in β†’ 1 out7.3300 XPM109 B
AQg7z8sS…egoK1Q8M
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.

3.769 Γ— 10⁹⁡(96-digit number)
37697255324928311923…20186940675869798120
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
3.769 Γ— 10⁹⁡(96-digit number)
37697255324928311923…20186940675869798121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.539 Γ— 10⁹⁡(96-digit number)
75394510649856623846…40373881351739596241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.507 Γ— 10⁹⁢(97-digit number)
15078902129971324769…80747762703479192481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.015 Γ— 10⁹⁢(97-digit number)
30157804259942649538…61495525406958384961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.031 Γ— 10⁹⁢(97-digit number)
60315608519885299077…22991050813916769921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.206 Γ— 10⁹⁷(98-digit number)
12063121703977059815…45982101627833539841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.412 Γ— 10⁹⁷(98-digit number)
24126243407954119631…91964203255667079681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.825 Γ— 10⁹⁷(98-digit number)
48252486815908239262…83928406511334159361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.650 Γ— 10⁹⁷(98-digit number)
96504973631816478524…67856813022668318721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.930 Γ— 10⁹⁸(99-digit number)
19300994726363295704…35713626045336637441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.860 Γ— 10⁹⁸(99-digit number)
38601989452726591409…71427252090673274881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
7.720 Γ— 10⁹⁸(99-digit number)
77203978905453182819…42854504181346549761
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2866684

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 d69241cec61a3e4d49d76d08885d443047a87a23a3c3c5afd19e6058daa7f066

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 #2,866,684 on Chainz β†—
Circulating Supply:57,973,279 XPMΒ·at block #6,841,113 Β· updates every 60s
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