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Home/Chain Registry/Block #3,439,365

Block #3,439,365

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/19/2019, 7:21:14 AM Β· Difficulty 10.9789 Β· 3,402,583 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
919e5fc851cc8435aec5ee862e457f3ed7a4df02f357842d5344325b4458c34c
View on Chainz β†—

Difficulty

10.978856

Transactions

1

Size

201 B

Version

2

Bits

0afa964c

Nonce

739,600,688

Timestamp

11/19/2019, 7:21:14 AM

Confirmations

3,402,583

Merkle Root

fbe5cefd9ddb2e1b5b25717396e4b8878df7d1f3a911f15aaae7ffa3005a0411
Transactions (1)
Coinbasefbe5cefd9ddb2e…e7ffa3005a0411
1 in β†’ 1 out8.2800 XPM110 B
ASiq2qtK…VMhmk7yL
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.

3.854 Γ— 10⁹⁢(97-digit number)
38541682460055813542…11957024907101405440
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
3.854 Γ— 10⁹⁢(97-digit number)
38541682460055813542…11957024907101405439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.708 Γ— 10⁹⁢(97-digit number)
77083364920111627085…23914049814202810879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.541 Γ— 10⁹⁷(98-digit number)
15416672984022325417…47828099628405621759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.083 Γ— 10⁹⁷(98-digit number)
30833345968044650834…95656199256811243519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.166 Γ— 10⁹⁷(98-digit number)
61666691936089301668…91312398513622487039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.233 Γ— 10⁹⁸(99-digit number)
12333338387217860333…82624797027244974079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.466 Γ— 10⁹⁸(99-digit number)
24666676774435720667…65249594054489948159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.933 Γ— 10⁹⁸(99-digit number)
49333353548871441334…30499188108979896319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.866 Γ— 10⁹⁸(99-digit number)
98666707097742882668…60998376217959792639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.973 Γ— 10⁹⁹(100-digit number)
19733341419548576533…21996752435919585279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.946 Γ— 10⁹⁹(100-digit number)
39466682839097153067…43993504871839170559
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 3439365

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 919e5fc851cc8435aec5ee862e457f3ed7a4df02f357842d5344325b4458c34c

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 #3,439,365 on Chainz β†—
Circulating Supply:57,979,965 XPMΒ·at block #6,841,947 Β· updates every 60s
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