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Block #2,722,992

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/27/2018, 1:33:19 AM Β· Difficulty 11.6160 Β· 4,118,886 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ff20bb51a50658e3d2c825f04be41d8fe2fbb2da35d93551864b4eba781e468c
View on Chainz β†—

Difficulty

11.616047

Transactions

1

Size

200 B

Version

2

Bits

0b9db549

Nonce

1,934,816,741

Timestamp

6/27/2018, 1:33:19 AM

Confirmations

4,118,886

Merkle Root

e27cd937cfc3b5d489f1fb5076a1ff143ee58f3a7becddae92baff0ebffabeb6
Transactions (1)
Coinbasee27cd937cfc3b5…baff0ebffabeb6
1 in β†’ 1 out7.4000 XPM110 B
AMxKrGk7…g2ch3o6E
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.

2.443 Γ— 10⁹⁴(95-digit number)
24434556139960703391…08325153389668661770
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
2.443 Γ— 10⁹⁴(95-digit number)
24434556139960703391…08325153389668661769
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.886 Γ— 10⁹⁴(95-digit number)
48869112279921406783…16650306779337323539
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.773 Γ— 10⁹⁴(95-digit number)
97738224559842813566…33300613558674647079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.954 Γ— 10⁹⁡(96-digit number)
19547644911968562713…66601227117349294159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.909 Γ— 10⁹⁡(96-digit number)
39095289823937125426…33202454234698588319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.819 Γ— 10⁹⁡(96-digit number)
78190579647874250853…66404908469397176639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.563 Γ— 10⁹⁢(97-digit number)
15638115929574850170…32809816938794353279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.127 Γ— 10⁹⁢(97-digit number)
31276231859149700341…65619633877588706559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.255 Γ— 10⁹⁢(97-digit number)
62552463718299400682…31239267755177413119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.251 Γ— 10⁹⁷(98-digit number)
12510492743659880136…62478535510354826239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.502 Γ— 10⁹⁷(98-digit number)
25020985487319760273…24957071020709652479
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 2722992

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 ff20bb51a50658e3d2c825f04be41d8fe2fbb2da35d93551864b4eba781e468c

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 #2,722,992 on Chainz β†—
Circulating Supply:57,979,400 XPMΒ·at block #6,841,877 Β· updates every 60s
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