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Home/Chain Registry/Block #2,659,121

Block #2,659,121

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/13/2018, 9:45:54 AM Β· Difficulty 11.6456 Β· 4,183,854 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3ed645f945d3959bb9b445321a2dc77ea7134806eebb8f854d7b5cf9a6bddfbb
View on Chainz β†—

Difficulty

11.645564

Transactions

1

Size

201 B

Version

2

Bits

0ba543b6

Nonce

1,721,689,523

Timestamp

5/13/2018, 9:45:54 AM

Confirmations

4,183,854

Merkle Root

8eb129c825319e03ff63553e8b01d1c8305358520ab592e480be99dad8e87988
Transactions (1)
Coinbase8eb129c825319e…be99dad8e87988
1 in β†’ 1 out7.3600 XPM110 B
AQe6EPzW…1GtjXfYN
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.

3.315 Γ— 10⁹⁷(98-digit number)
33154285965548305620…44359541889211330560
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
3.315 Γ— 10⁹⁷(98-digit number)
33154285965548305620…44359541889211330559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.630 Γ— 10⁹⁷(98-digit number)
66308571931096611240…88719083778422661119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.326 Γ— 10⁹⁸(99-digit number)
13261714386219322248…77438167556845322239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.652 Γ— 10⁹⁸(99-digit number)
26523428772438644496…54876335113690644479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.304 Γ— 10⁹⁸(99-digit number)
53046857544877288992…09752670227381288959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.060 Γ— 10⁹⁹(100-digit number)
10609371508975457798…19505340454762577919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.121 Γ— 10⁹⁹(100-digit number)
21218743017950915596…39010680909525155839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.243 Γ— 10⁹⁹(100-digit number)
42437486035901831193…78021361819050311679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.487 Γ— 10⁹⁹(100-digit number)
84874972071803662387…56042723638100623359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.697 Γ— 10¹⁰⁰(101-digit number)
16974994414360732477…12085447276201246719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.394 Γ— 10¹⁰⁰(101-digit number)
33949988828721464954…24170894552402493439
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 2659121

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 3ed645f945d3959bb9b445321a2dc77ea7134806eebb8f854d7b5cf9a6bddfbb

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 #2,659,121 on Chainz β†—
Circulating Supply:57,988,153 XPMΒ·at block #6,842,974 Β· updates every 60s
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