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Block #2,783,872

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2018, 9:16:36 PM Β· Difficulty 11.6650 Β· 4,058,808 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c4710c7c6bf0b8be28f4c7b18d0980ee922e4f9ac7ec58db3ecd0991474fd9a4
View on Chainz β†—

Difficulty

11.665029

Transactions

1

Size

200 B

Version

2

Bits

0baa3f54

Nonce

110,322,173

Timestamp

8/7/2018, 9:16:36 PM

Confirmations

4,058,808

Merkle Root

8ea08727a1adea5fe8be6001b76fe6ff3dbae402b89d08bd17b9b802ea6039ce
Transactions (1)
Coinbase8ea08727a1adea…b9b802ea6039ce
1 in β†’ 1 out7.3400 XPM110 B
AGkAWXrR…Djq41bFJ
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.

1.222 Γ— 10⁹⁡(96-digit number)
12225650666826189830…41220203468225748370
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
1.222 Γ— 10⁹⁡(96-digit number)
12225650666826189830…41220203468225748369
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.445 Γ— 10⁹⁡(96-digit number)
24451301333652379660…82440406936451496739
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.890 Γ— 10⁹⁡(96-digit number)
48902602667304759320…64880813872902993479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.780 Γ— 10⁹⁡(96-digit number)
97805205334609518640…29761627745805986959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.956 Γ— 10⁹⁢(97-digit number)
19561041066921903728…59523255491611973919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.912 Γ— 10⁹⁢(97-digit number)
39122082133843807456…19046510983223947839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.824 Γ— 10⁹⁢(97-digit number)
78244164267687614912…38093021966447895679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.564 Γ— 10⁹⁷(98-digit number)
15648832853537522982…76186043932895791359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.129 Γ— 10⁹⁷(98-digit number)
31297665707075045964…52372087865791582719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.259 Γ— 10⁹⁷(98-digit number)
62595331414150091929…04744175731583165439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.251 Γ— 10⁹⁸(99-digit number)
12519066282830018385…09488351463166330879
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 2783872

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 c4710c7c6bf0b8be28f4c7b18d0980ee922e4f9ac7ec58db3ecd0991474fd9a4

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 #2,783,872 on Chainz β†—
Circulating Supply:57,985,876 XPMΒ·at block #6,842,679 Β· updates every 60s
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