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Block #2,778,728

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/4/2018, 11:21:55 AM Β· Difficulty 11.6492 Β· 4,061,189 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f2219fdf9fbb0b211a9105f44fa9ec1837d0aaf67fe75338f2f2772dd4a88857
View on Chainz β†—

Difficulty

11.649191

Transactions

1

Size

200 B

Version

2

Bits

0ba63160

Nonce

245,977,729

Timestamp

8/4/2018, 11:21:55 AM

Confirmations

4,061,189

Merkle Root

09a701796d85f2a8bed40fda4935ef2ad440452efed584e11574ff39909debda
Transactions (1)
Coinbase09a701796d85f2…74ff39909debda
1 in β†’ 1 out7.3600 XPM110 B
AZtxQr2F…7grUWrUz
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.

6.198 Γ— 10⁹³(94-digit number)
61986048840562845028…00489779042114000640
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
6.198 Γ— 10⁹³(94-digit number)
61986048840562845028…00489779042114000639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.239 Γ— 10⁹⁴(95-digit number)
12397209768112569005…00979558084228001279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.479 Γ— 10⁹⁴(95-digit number)
24794419536225138011…01959116168456002559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.958 Γ— 10⁹⁴(95-digit number)
49588839072450276022…03918232336912005119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.917 Γ— 10⁹⁴(95-digit number)
99177678144900552045…07836464673824010239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.983 Γ— 10⁹⁡(96-digit number)
19835535628980110409…15672929347648020479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.967 Γ— 10⁹⁡(96-digit number)
39671071257960220818…31345858695296040959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.934 Γ— 10⁹⁡(96-digit number)
79342142515920441636…62691717390592081919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.586 Γ— 10⁹⁢(97-digit number)
15868428503184088327…25383434781184163839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.173 Γ— 10⁹⁢(97-digit number)
31736857006368176654…50766869562368327679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.347 Γ— 10⁹⁢(97-digit number)
63473714012736353308…01533739124736655359
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 2778728

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 f2219fdf9fbb0b211a9105f44fa9ec1837d0aaf67fe75338f2f2772dd4a88857

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 #2,778,728 on Chainz β†—
Circulating Supply:57,963,637 XPMΒ·at block #6,839,916 Β· updates every 60s
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