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Home/Chain Registry/Block #2,666,331

Block #2,666,331

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/18/2018, 4:59:31 AM Β· Difficulty 11.6660 Β· 4,174,067 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
767cea146385757743f534b180dc541cf26d29bb6a27a9a3f6fce60217dfc5de
View on Chainz β†—

Difficulty

11.666026

Transactions

1

Size

200 B

Version

2

Bits

0baa80a7

Nonce

1,944,071,609

Timestamp

5/18/2018, 4:59:31 AM

Confirmations

4,174,067

Merkle Root

d380038f6d2bda54ac2736cd9e758d37d7bba8f5f05d1056460c2847232f6ad6
Transactions (1)
Coinbased380038f6d2bda…0c2847232f6ad6
1 in β†’ 1 out7.3400 XPM110 B
AJHsSfTS…mV1Wax3B
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.

8.894 Γ— 10⁹⁴(95-digit number)
88945210246062807826…91055772262022800710
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
8.894 Γ— 10⁹⁴(95-digit number)
88945210246062807826…91055772262022800709
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.778 Γ— 10⁹⁡(96-digit number)
17789042049212561565…82111544524045601419
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.557 Γ— 10⁹⁡(96-digit number)
35578084098425123130…64223089048091202839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.115 Γ— 10⁹⁡(96-digit number)
71156168196850246261…28446178096182405679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.423 Γ— 10⁹⁢(97-digit number)
14231233639370049252…56892356192364811359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.846 Γ— 10⁹⁢(97-digit number)
28462467278740098504…13784712384729622719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.692 Γ— 10⁹⁢(97-digit number)
56924934557480197008…27569424769459245439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.138 Γ— 10⁹⁷(98-digit number)
11384986911496039401…55138849538918490879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.276 Γ— 10⁹⁷(98-digit number)
22769973822992078803…10277699077836981759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.553 Γ— 10⁹⁷(98-digit number)
45539947645984157607…20555398155673963519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.107 Γ— 10⁹⁷(98-digit number)
91079895291968315214…41110796311347927039
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 2666331

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 767cea146385757743f534b180dc541cf26d29bb6a27a9a3f6fce60217dfc5de

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 #2,666,331 on Chainz β†—
Circulating Supply:57,967,506 XPMΒ·at block #6,840,397 Β· updates every 60s
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