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Home/Chain Registry/Block #3,242,280

Block #3,242,280

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/26/2019, 9:16:20 PM Β· Difficulty 11.0020 Β· 3,602,715 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
df96a2aded68fbb743ec8c7e9f3866c85f4e1757f7cd6bdd9ac5c9fc9623c4c9
View on Chainz β†—

Difficulty

11.001971

Transactions

1

Size

200 B

Version

2

Bits

0b008134

Nonce

1,634,853,786

Timestamp

6/26/2019, 9:16:20 PM

Confirmations

3,602,715

Merkle Root

8eeb8d83f3042e896586c93e53ba8cbc7e7dab1dd928f7c0e1f1f7ca0b932ae7
Transactions (1)
Coinbase8eeb8d83f3042e…f1f7ca0b932ae7
1 in β†’ 1 out8.2500 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.

3.825 Γ— 10⁹⁡(96-digit number)
38253118083003684612…69000608335944958720
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
3.825 Γ— 10⁹⁡(96-digit number)
38253118083003684612…69000608335944958719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.650 Γ— 10⁹⁡(96-digit number)
76506236166007369225…38001216671889917439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.530 Γ— 10⁹⁢(97-digit number)
15301247233201473845…76002433343779834879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.060 Γ— 10⁹⁢(97-digit number)
30602494466402947690…52004866687559669759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.120 Γ— 10⁹⁢(97-digit number)
61204988932805895380…04009733375119339519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.224 Γ— 10⁹⁷(98-digit number)
12240997786561179076…08019466750238679039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.448 Γ— 10⁹⁷(98-digit number)
24481995573122358152…16038933500477358079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.896 Γ— 10⁹⁷(98-digit number)
48963991146244716304…32077867000954716159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.792 Γ— 10⁹⁷(98-digit number)
97927982292489432608…64155734001909432319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.958 Γ— 10⁹⁸(99-digit number)
19585596458497886521…28311468003818864639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.917 Γ— 10⁹⁸(99-digit number)
39171192916995773043…56622936007637729279
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 3242280

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 df96a2aded68fbb743ec8c7e9f3866c85f4e1757f7cd6bdd9ac5c9fc9623c4c9

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 #3,242,280 on Chainz β†—
Circulating Supply:58,004,381 XPMΒ·at block #6,844,994 Β· updates every 60s
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