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Block #1,482,218

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/3/2016, 6:35:17 PM Β· Difficulty 10.7272 Β· 5,360,772 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a2bbea4497fbdd8893cdfd5971e04275d60832e9bf5080d7482fcdf204a67506
View on Chainz β†—

Difficulty

10.727247

Transactions

1

Size

198 B

Version

2

Bits

0aba2cdb

Nonce

1,664,577,128

Timestamp

3/3/2016, 6:35:17 PM

Confirmations

5,360,772

Merkle Root

236c32efe5f1b9c18f92765ceb6e8015e7c6841726ce3d3ac3849aca07f436d4
Transactions (1)
Coinbase236c32efe5f1b9…849aca07f436d4
1 in β†’ 1 out8.6800 XPM109 B
AH8yL8RW…W2zUguvv
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.

1.466 Γ— 10⁹³(94-digit number)
14666334079227642687…60582169553781745920
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
1.466 Γ— 10⁹³(94-digit number)
14666334079227642687…60582169553781745921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.933 Γ— 10⁹³(94-digit number)
29332668158455285374…21164339107563491841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.866 Γ— 10⁹³(94-digit number)
58665336316910570749…42328678215126983681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.173 Γ— 10⁹⁴(95-digit number)
11733067263382114149…84657356430253967361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.346 Γ— 10⁹⁴(95-digit number)
23466134526764228299…69314712860507934721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.693 Γ— 10⁹⁴(95-digit number)
46932269053528456599…38629425721015869441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.386 Γ— 10⁹⁴(95-digit number)
93864538107056913198…77258851442031738881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.877 Γ— 10⁹⁡(96-digit number)
18772907621411382639…54517702884063477761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.754 Γ— 10⁹⁡(96-digit number)
37545815242822765279…09035405768126955521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.509 Γ— 10⁹⁡(96-digit number)
75091630485645530558…18070811536253911041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1482218

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 a2bbea4497fbdd8893cdfd5971e04275d60832e9bf5080d7482fcdf204a67506

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 #1,482,218 on Chainz β†—
Circulating Supply:57,988,276 XPMΒ·at block #6,842,989 Β· updates every 60s
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