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Home/Chain Registry/Block #3,240,619

Block #3,240,619

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/25/2019, 5:23:50 PM Β· Difficulty 11.0033 Β· 3,604,651 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
000c928fe2830c4e923e0e1761e25cbc960472e5edd64c40ca5909cfbfa28210
View on Chainz β†—

Difficulty

11.003320

Transactions

1

Size

200 B

Version

2

Bits

0b00d98e

Nonce

1,125,220,254

Timestamp

6/25/2019, 5:23:50 PM

Confirmations

3,604,651

Merkle Root

357ee2e311e29d29ce81c1cafb3f94da2e4574fd3c1fc51264b4357999a2fa29
Transactions (1)
Coinbase357ee2e311e29d…b4357999a2fa29
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.

2.023 Γ— 10⁹⁴(95-digit number)
20232333126366604446…59778648785062935160
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
2.023 Γ— 10⁹⁴(95-digit number)
20232333126366604446…59778648785062935159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.046 Γ— 10⁹⁴(95-digit number)
40464666252733208893…19557297570125870319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.092 Γ— 10⁹⁴(95-digit number)
80929332505466417786…39114595140251740639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.618 Γ— 10⁹⁡(96-digit number)
16185866501093283557…78229190280503481279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.237 Γ— 10⁹⁡(96-digit number)
32371733002186567114…56458380561006962559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.474 Γ— 10⁹⁡(96-digit number)
64743466004373134229…12916761122013925119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.294 Γ— 10⁹⁢(97-digit number)
12948693200874626845…25833522244027850239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.589 Γ— 10⁹⁢(97-digit number)
25897386401749253691…51667044488055700479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.179 Γ— 10⁹⁢(97-digit number)
51794772803498507383…03334088976111400959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.035 Γ— 10⁹⁷(98-digit number)
10358954560699701476…06668177952222801919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.071 Γ— 10⁹⁷(98-digit number)
20717909121399402953…13336355904445603839
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 3240619

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 000c928fe2830c4e923e0e1761e25cbc960472e5edd64c40ca5909cfbfa28210

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 #3,240,619 on Chainz β†—
Circulating Supply:58,006,595 XPMΒ·at block #6,845,269 Β· updates every 60s
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