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Home/Chain Registry/Block #3,001,736

Block #3,001,736

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/9/2019, 6:21:14 AM Β· Difficulty 11.2070 Β· 3,829,737 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f0fd37199a0e219ffcc198f93f431c55eee5388d54774d80e0a669c0e9b52a75
View on Chainz β†—

Difficulty

11.206982

Transactions

1

Size

200 B

Version

2

Bits

0b34fccd

Nonce

50,556,643

Timestamp

1/9/2019, 6:21:14 AM

Confirmations

3,829,737

Merkle Root

f3163c3c1b279dd6e3b990ea8b1c5c3ef267fbb30aa09691fa53de4498897c5d
Transactions (1)
Coinbasef3163c3c1b279d…53de4498897c5d
1 in β†’ 1 out7.9500 XPM110 B
AUMQRepm…tAfKmdW1
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.

2.228 Γ— 10⁹⁡(96-digit number)
22280347172456937051…40301354763272501760
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
2.228 Γ— 10⁹⁡(96-digit number)
22280347172456937051…40301354763272501759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.456 Γ— 10⁹⁡(96-digit number)
44560694344913874102…80602709526545003519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.912 Γ— 10⁹⁡(96-digit number)
89121388689827748204…61205419053090007039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.782 Γ— 10⁹⁢(97-digit number)
17824277737965549640…22410838106180014079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.564 Γ— 10⁹⁢(97-digit number)
35648555475931099281…44821676212360028159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.129 Γ— 10⁹⁢(97-digit number)
71297110951862198563…89643352424720056319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.425 Γ— 10⁹⁷(98-digit number)
14259422190372439712…79286704849440112639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.851 Γ— 10⁹⁷(98-digit number)
28518844380744879425…58573409698880225279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.703 Γ— 10⁹⁷(98-digit number)
57037688761489758850…17146819397760450559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.140 Γ— 10⁹⁸(99-digit number)
11407537752297951770…34293638795520901119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.281 Γ— 10⁹⁸(99-digit number)
22815075504595903540…68587277591041802239
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 3001736

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 f0fd37199a0e219ffcc198f93f431c55eee5388d54774d80e0a669c0e9b52a75

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 #3,001,736 on Chainz β†—
Circulating Supply:57,895,875 XPMΒ·at block #6,831,472 Β· updates every 60s
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