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Block #2,649,476

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/5/2018, 6:51:27 AM Β· Difficulty 11.7637 Β· 4,183,241 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
21770d1eee2f5c86d12565b63beaf9cf6cae80a347da7e3d56e1ee3cd00618c3
View on Chainz β†—

Difficulty

11.763668

Transactions

1

Size

201 B

Version

2

Bits

0bc37fc5

Nonce

855,278,337

Timestamp

5/5/2018, 6:51:27 AM

Confirmations

4,183,241

Merkle Root

375abac62819ceed2d2b71f8ce4f81bdbf48cfb5fa0f6ed7ee0168b7c6b93bfb
Transactions (1)
Coinbase375abac62819ce…0168b7c6b93bfb
1 in β†’ 1 out7.2100 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.

1.000 Γ— 10⁹⁢(97-digit number)
10006780821240933318…11923187125560516560
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
1.000 Γ— 10⁹⁢(97-digit number)
10006780821240933318…11923187125560516561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.001 Γ— 10⁹⁢(97-digit number)
20013561642481866637…23846374251121033121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.002 Γ— 10⁹⁢(97-digit number)
40027123284963733274…47692748502242066241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.005 Γ— 10⁹⁢(97-digit number)
80054246569927466548…95385497004484132481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.601 Γ— 10⁹⁷(98-digit number)
16010849313985493309…90770994008968264961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.202 Γ— 10⁹⁷(98-digit number)
32021698627970986619…81541988017936529921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.404 Γ— 10⁹⁷(98-digit number)
64043397255941973238…63083976035873059841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.280 Γ— 10⁹⁸(99-digit number)
12808679451188394647…26167952071746119681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.561 Γ— 10⁹⁸(99-digit number)
25617358902376789295…52335904143492239361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.123 Γ— 10⁹⁸(99-digit number)
51234717804753578590…04671808286984478721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.024 Γ— 10⁹⁹(100-digit number)
10246943560950715718…09343616573968957441
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 2649476

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 21770d1eee2f5c86d12565b63beaf9cf6cae80a347da7e3d56e1ee3cd00618c3

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 #2,649,476 on Chainz β†—
Circulating Supply:57,905,896 XPMΒ·at block #6,832,716 Β· updates every 60s
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