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Home/Chain Registry/Block #2,649,960

Block #2,649,960

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/5/2018, 4:02:56 PM Β· Difficulty 11.7605 Β· 4,191,166 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b17c570919aa1d23c82adcd047f5630d9b5c0f84864e0432f4dfc7fcfd05ca56
View on Chainz β†—

Difficulty

11.760538

Transactions

2

Size

426 B

Version

2

Bits

0bc2b297

Nonce

1,853,684,466

Timestamp

5/5/2018, 4:02:56 PM

Confirmations

4,191,166

Merkle Root

b5f44e7c98d179f482e847aecddf204e510d058104182fcf7f9fa6b157ec5687
Transactions (2)
Coinbase38f90f2a87dc10…869575e50e53b8
1 in β†’ 1 out7.2300 XPM110 B
AQhcUSsK…Ti41wqNd
b4f23f8744ba4b…ad8222ed454b2c
1 in β†’ 2 out3.0383 XPM226 B
ALvrNVZd…WWVpyiCuAJtZD9s1…k6VbFMvR
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.

3.485 Γ— 10⁹⁴(95-digit number)
34853440173905940143…87077246503580012120
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
3.485 Γ— 10⁹⁴(95-digit number)
34853440173905940143…87077246503580012119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.970 Γ— 10⁹⁴(95-digit number)
69706880347811880286…74154493007160024239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.394 Γ— 10⁹⁡(96-digit number)
13941376069562376057…48308986014320048479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.788 Γ— 10⁹⁡(96-digit number)
27882752139124752114…96617972028640096959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.576 Γ— 10⁹⁡(96-digit number)
55765504278249504228…93235944057280193919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.115 Γ— 10⁹⁢(97-digit number)
11153100855649900845…86471888114560387839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.230 Γ— 10⁹⁢(97-digit number)
22306201711299801691…72943776229120775679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.461 Γ— 10⁹⁢(97-digit number)
44612403422599603383…45887552458241551359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.922 Γ— 10⁹⁢(97-digit number)
89224806845199206766…91775104916483102719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.784 Γ— 10⁹⁷(98-digit number)
17844961369039841353…83550209832966205439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.568 Γ— 10⁹⁷(98-digit number)
35689922738079682706…67100419665932410879
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 2649960

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 b17c570919aa1d23c82adcd047f5630d9b5c0f84864e0432f4dfc7fcfd05ca56

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 #2,649,960 on Chainz β†—
Circulating Supply:57,973,377 XPMΒ·at block #6,841,125 Β· updates every 60s
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