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Block #1,482,214

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/3/2016, 6:31:33 PM Β· Difficulty 10.7272 Β· 5,362,823 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
82ddd2670fc81912336e3bdb5ef6d05e6b5b044ce28adacee52237ba92531edb
View on Chainz β†—

Difficulty

10.727223

Transactions

1

Size

242 B

Version

2

Bits

0aba2b4f

Nonce

22,177,123

Timestamp

3/3/2016, 6:31:33 PM

Confirmations

5,362,823

Merkle Root

c4ed5de0b26b9e11cfb36cd7b448f012e93599d994d572a4cfdb9c5df2046f3b
Transactions (1)
Coinbasec4ed5de0b26b9e…db9c5df2046f3b
1 in β†’ 2 out8.6800 XPM152 B
AJhBJVbg…GPMa5GurALPu3s2c…EJXLjVFh
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.

8.550 Γ— 10⁹⁴(95-digit number)
85500391455788660750…95021345436409392080
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
8.550 Γ— 10⁹⁴(95-digit number)
85500391455788660750…95021345436409392079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.710 Γ— 10⁹⁡(96-digit number)
17100078291157732150…90042690872818784159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.420 Γ— 10⁹⁡(96-digit number)
34200156582315464300…80085381745637568319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.840 Γ— 10⁹⁡(96-digit number)
68400313164630928600…60170763491275136639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.368 Γ— 10⁹⁢(97-digit number)
13680062632926185720…20341526982550273279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.736 Γ— 10⁹⁢(97-digit number)
27360125265852371440…40683053965100546559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.472 Γ— 10⁹⁢(97-digit number)
54720250531704742880…81366107930201093119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.094 Γ— 10⁹⁷(98-digit number)
10944050106340948576…62732215860402186239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.188 Γ— 10⁹⁷(98-digit number)
21888100212681897152…25464431720804372479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.377 Γ— 10⁹⁷(98-digit number)
43776200425363794304…50928863441608744959
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 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
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 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 1482214

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 82ddd2670fc81912336e3bdb5ef6d05e6b5b044ce28adacee52237ba92531edb

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 #1,482,214 on Chainz β†—
Circulating Supply:58,004,723 XPMΒ·at block #6,845,036 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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