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Block #2,638,990

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 12:01:43 PM Β· Difficulty 11.5171 Β· 4,200,691 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2f46dfa223da1a4d6a961ddeac2ed038c0f65d79142529eac8540819e0f917eb
View on Chainz β†—

Difficulty

11.517092

Transactions

1

Size

200 B

Version

2

Bits

0b846023

Nonce

409,954,126

Timestamp

4/30/2018, 12:01:43 PM

Confirmations

4,200,691

Merkle Root

b781d239f5880dd134d9a0572a36533619875dbe47834dd7ed580af199b32474
Transactions (1)
Coinbaseb781d239f5880d…580af199b32474
1 in β†’ 1 out7.5300 XPM110 B
Adqah8zh…1WwoHJ9t
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.

2.719 Γ— 10⁹⁴(95-digit number)
27195556968180367317…85154554787784009440
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.719 Γ— 10⁹⁴(95-digit number)
27195556968180367317…85154554787784009441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.439 Γ— 10⁹⁴(95-digit number)
54391113936360734634…70309109575568018881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.087 Γ— 10⁹⁡(96-digit number)
10878222787272146926…40618219151136037761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.175 Γ— 10⁹⁡(96-digit number)
21756445574544293853…81236438302272075521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.351 Γ— 10⁹⁡(96-digit number)
43512891149088587707…62472876604544151041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.702 Γ— 10⁹⁡(96-digit number)
87025782298177175414…24945753209088302081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.740 Γ— 10⁹⁢(97-digit number)
17405156459635435082…49891506418176604161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.481 Γ— 10⁹⁢(97-digit number)
34810312919270870165…99783012836353208321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.962 Γ— 10⁹⁢(97-digit number)
69620625838541740331…99566025672706416641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.392 Γ— 10⁹⁷(98-digit number)
13924125167708348066…99132051345412833281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.784 Γ— 10⁹⁷(98-digit number)
27848250335416696132…98264102690825666561
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2638990

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 2f46dfa223da1a4d6a961ddeac2ed038c0f65d79142529eac8540819e0f917eb

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 #2,638,990 on Chainz β†—
Circulating Supply:57,961,735 XPMΒ·at block #6,839,680 Β· updates every 60s
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