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Home/Chain Registry/Block #3,503,814

Block #3,503,814

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/7/2020, 11:42:24 AM Β· Difficulty 10.9308 Β· 3,340,945 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4877475baa9f03793a55cf8e2e45e02e7cd23541d70d7446cfe100eb6673e6d4
View on Chainz β†—

Difficulty

10.930773

Transactions

1

Size

201 B

Version

2

Bits

0aee4721

Nonce

1,220,901,319

Timestamp

1/7/2020, 11:42:24 AM

Confirmations

3,340,945

Merkle Root

9cd60318f6f7f3a9361bf759c71d0d698907af27b3a3efd530609daa1f3c509b
Transactions (1)
Coinbase9cd60318f6f7f3…609daa1f3c509b
1 in β†’ 1 out8.3600 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.

7.652 Γ— 10⁹⁢(97-digit number)
76528771140904479231…57641144575149690880
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
7.652 Γ— 10⁹⁢(97-digit number)
76528771140904479231…57641144575149690879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.530 Γ— 10⁹⁷(98-digit number)
15305754228180895846…15282289150299381759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.061 Γ— 10⁹⁷(98-digit number)
30611508456361791692…30564578300598763519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.122 Γ— 10⁹⁷(98-digit number)
61223016912723583385…61129156601197527039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.224 Γ— 10⁹⁸(99-digit number)
12244603382544716677…22258313202395054079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.448 Γ— 10⁹⁸(99-digit number)
24489206765089433354…44516626404790108159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.897 Γ— 10⁹⁸(99-digit number)
48978413530178866708…89033252809580216319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.795 Γ— 10⁹⁸(99-digit number)
97956827060357733416…78066505619160432639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.959 Γ— 10⁹⁹(100-digit number)
19591365412071546683…56133011238320865279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.918 Γ— 10⁹⁹(100-digit number)
39182730824143093366…12266022476641730559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.836 Γ— 10⁹⁹(100-digit number)
78365461648286186733…24532044953283461119
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 3503814

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 4877475baa9f03793a55cf8e2e45e02e7cd23541d70d7446cfe100eb6673e6d4

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 #3,503,814 on Chainz β†—
Circulating Supply:58,002,483 XPMΒ·at block #6,844,758 Β· updates every 60s
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