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Home/Chain Registry/Block #2,611,450

Block #2,611,450

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/13/2018, 1:40:53 AM Β· Difficulty 11.2154 Β· 4,222,073 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
303d34b95cf9b7f2355aa032c35301f9a5d52f938868524b9b293fc52b660dd5
View on Chainz β†—

Difficulty

11.215394

Transactions

2

Size

20.92 KB

Version

2

Bits

0b372412

Nonce

834,045,696

Timestamp

4/13/2018, 1:40:53 AM

Confirmations

4,222,073

Merkle Root

e0fd7bfdb19cc14c76fef9b0ef9ee2176ab956d6c2cd315151d91d2a2a3e2641
Transactions (2)
Coinbase73bf157cfc08de…81c3a69f0242ec
1 in β†’ 1 out8.1600 XPM109 B
AGLX4oJF…a2uXD1eM
1d4596ef3911a1…7e99bd16046933
143 in β†’ 2 out1436.7116 XPM20.73 KB
ATsGpLaK…6ivo8bfZARcKMnmT…5BLzvoTF
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.

8.445 Γ— 10⁹²(93-digit number)
84456143199737689647…38722091857524887680
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
8.445 Γ— 10⁹²(93-digit number)
84456143199737689647…38722091857524887679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.689 Γ— 10⁹³(94-digit number)
16891228639947537929…77444183715049775359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.378 Γ— 10⁹³(94-digit number)
33782457279895075859…54888367430099550719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.756 Γ— 10⁹³(94-digit number)
67564914559790151718…09776734860199101439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.351 Γ— 10⁹⁴(95-digit number)
13512982911958030343…19553469720398202879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.702 Γ— 10⁹⁴(95-digit number)
27025965823916060687…39106939440796405759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.405 Γ— 10⁹⁴(95-digit number)
54051931647832121374…78213878881592811519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.081 Γ— 10⁹⁡(96-digit number)
10810386329566424274…56427757763185623039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.162 Γ— 10⁹⁡(96-digit number)
21620772659132848549…12855515526371246079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.324 Γ— 10⁹⁡(96-digit number)
43241545318265697099…25711031052742492159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.648 Γ— 10⁹⁡(96-digit number)
86483090636531394199…51422062105484984319
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 2611450

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 303d34b95cf9b7f2355aa032c35301f9a5d52f938868524b9b293fc52b660dd5

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 #2,611,450 on Chainz β†—
Circulating Supply:57,912,384 XPMΒ·at block #6,833,522 Β· updates every 60s
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