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Home/Chain Registry/Block #2,730,669

Block #2,730,669

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/2/2018, 6:04:29 AM Β· Difficulty 11.6317 Β· 4,109,783 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
82bec5d65b9334d33eb9dd8e83f653af7e3268208debf6b4b1bc74ee1f174a90
View on Chainz β†—

Difficulty

11.631678

Transactions

1

Size

199 B

Version

2

Bits

0ba1b5a1

Nonce

289,429,363

Timestamp

7/2/2018, 6:04:29 AM

Confirmations

4,109,783

Merkle Root

18452c8237e8b258ec21d9a8edd496b3bbaa62666818fd5eab9aa27b32b407a8
Transactions (1)
Coinbase18452c8237e8b2…9aa27b32b407a8
1 in β†’ 1 out7.3800 XPM110 B
AP3ksNDX…CRfueLGd
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.

9.274 Γ— 10⁹²(93-digit number)
92746082114348193252…94736494602808867680
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
9.274 Γ— 10⁹²(93-digit number)
92746082114348193252…94736494602808867679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.854 Γ— 10⁹³(94-digit number)
18549216422869638650…89472989205617735359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.709 Γ— 10⁹³(94-digit number)
37098432845739277300…78945978411235470719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.419 Γ— 10⁹³(94-digit number)
74196865691478554601…57891956822470941439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.483 Γ— 10⁹⁴(95-digit number)
14839373138295710920…15783913644941882879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.967 Γ— 10⁹⁴(95-digit number)
29678746276591421840…31567827289883765759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.935 Γ— 10⁹⁴(95-digit number)
59357492553182843681…63135654579767531519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.187 Γ— 10⁹⁡(96-digit number)
11871498510636568736…26271309159535063039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.374 Γ— 10⁹⁡(96-digit number)
23742997021273137472…52542618319070126079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.748 Γ— 10⁹⁡(96-digit number)
47485994042546274945…05085236638140252159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.497 Γ— 10⁹⁡(96-digit number)
94971988085092549890…10170473276280504319
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2730669

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 82bec5d65b9334d33eb9dd8e83f653af7e3268208debf6b4b1bc74ee1f174a90

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 #2,730,669 on Chainz β†—
Circulating Supply:57,967,947 XPMΒ·at block #6,840,451 Β· updates every 60s
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