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Home/Chain Registry/Block #2,690,266

Block #2,690,266

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/3/2018, 3:31:23 PM Β· Difficulty 11.6840 Β· 4,152,649 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8da390f630dffcfdd6c4cb22e2555bc17f6903ece8397a78fe8d83325ae6b838
View on Chainz β†—

Difficulty

11.683954

Transactions

2

Size

572 B

Version

2

Bits

0baf179e

Nonce

1,576,685,613

Timestamp

6/3/2018, 3:31:23 PM

Confirmations

4,152,649

Merkle Root

180cea684e522c282a3a3a3eeacc1d37529f55d6fb56643a89b01bfc9360f78e
Transactions (2)
Coinbase60f6dd4ffc0bb5…bd5a5ac3083f30
1 in β†’ 1 out7.3200 XPM110 B
AScqPvVQ…X4TTXwYv
03114cf5ae31a0…2523f2e8757db9
2 in β†’ 2 out8.0109 XPM373 B
AQLjudh6…KMxjBYPLAbYGwLjD…o5yNpDYA
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.

9.196 Γ— 10⁹²(93-digit number)
91965313517873304324…75401003558758654120
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
9.196 Γ— 10⁹²(93-digit number)
91965313517873304324…75401003558758654121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.839 Γ— 10⁹³(94-digit number)
18393062703574660864…50802007117517308241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.678 Γ— 10⁹³(94-digit number)
36786125407149321729…01604014235034616481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.357 Γ— 10⁹³(94-digit number)
73572250814298643459…03208028470069232961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.471 Γ— 10⁹⁴(95-digit number)
14714450162859728691…06416056940138465921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.942 Γ— 10⁹⁴(95-digit number)
29428900325719457383…12832113880276931841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.885 Γ— 10⁹⁴(95-digit number)
58857800651438914767…25664227760553863681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.177 Γ— 10⁹⁡(96-digit number)
11771560130287782953…51328455521107727361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.354 Γ— 10⁹⁡(96-digit number)
23543120260575565907…02656911042215454721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.708 Γ— 10⁹⁡(96-digit number)
47086240521151131814…05313822084430909441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.417 Γ— 10⁹⁡(96-digit number)
94172481042302263628…10627644168861818881
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 2690266

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 8da390f630dffcfdd6c4cb22e2555bc17f6903ece8397a78fe8d83325ae6b838

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 #2,690,266 on Chainz β†—
Circulating Supply:57,987,668 XPMΒ·at block #6,842,914 Β· updates every 60s
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