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Block #3,472,432

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/12/2019, 9:46:57 AM Β· Difficulty 10.9790 Β· 3,342,087 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
35289280e8156943404d1b5c7aa5a9d1f39b032e35bca122ff3e96b369739166
View on Chainz β†—

Difficulty

10.979012

Transactions

1

Size

201 B

Version

2

Bits

0afaa08f

Nonce

1,941,959,824

Timestamp

12/12/2019, 9:46:57 AM

Confirmations

3,342,087

Merkle Root

dc2d781d882121648a724058034d1c37a892c60095467dfc3b1bf1ae4cb6d979
Transactions (1)
Coinbasedc2d781d882121…1bf1ae4cb6d979
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.

1.260 Γ— 10⁹⁢(97-digit number)
12600055578833315135…71804779136494088960
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
1.260 Γ— 10⁹⁢(97-digit number)
12600055578833315135…71804779136494088959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.520 Γ— 10⁹⁢(97-digit number)
25200111157666630270…43609558272988177919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.040 Γ— 10⁹⁢(97-digit number)
50400222315333260540…87219116545976355839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.008 Γ— 10⁹⁷(98-digit number)
10080044463066652108…74438233091952711679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.016 Γ— 10⁹⁷(98-digit number)
20160088926133304216…48876466183905423359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.032 Γ— 10⁹⁷(98-digit number)
40320177852266608432…97752932367810846719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.064 Γ— 10⁹⁷(98-digit number)
80640355704533216865…95505864735621693439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.612 Γ— 10⁹⁸(99-digit number)
16128071140906643373…91011729471243386879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.225 Γ— 10⁹⁸(99-digit number)
32256142281813286746…82023458942486773759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.451 Γ— 10⁹⁸(99-digit number)
64512284563626573492…64046917884973547519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.290 Γ— 10⁹⁹(100-digit number)
12902456912725314698…28093835769947095039
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 3472432

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 35289280e8156943404d1b5c7aa5a9d1f39b032e35bca122ff3e96b369739166

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 #3,472,432 on Chainz β†—
Circulating Supply:57,760,220 XPMΒ·at block #6,814,518 Β· updates every 60s
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