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Home/Chain Registry/Block #2,649,480

Block #2,649,480

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/5/2018, 6:54:56 AM Β· Difficulty 11.7637 Β· 4,183,751 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4083f0a6095b1b982a0622c2b28290737edce680e9f533afb8949e618ca9cade
View on Chainz β†—

Difficulty

11.763701

Transactions

1

Size

200 B

Version

2

Bits

0bc381ed

Nonce

653,743,373

Timestamp

5/5/2018, 6:54:56 AM

Confirmations

4,183,751

Merkle Root

52aded5d42ba256f0937bcbf2adff679e914fa61e839ddf2924d0f0a3d6fd2af
Transactions (1)
Coinbase52aded5d42ba25…4d0f0a3d6fd2af
1 in β†’ 1 out7.2100 XPM110 B
AXDmuW8X…wr54kBNR
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.

1.747 Γ— 10⁹⁴(95-digit number)
17478309217707842812…82817353580184160000
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
1.747 Γ— 10⁹⁴(95-digit number)
17478309217707842812…82817353580184159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.495 Γ— 10⁹⁴(95-digit number)
34956618435415685624…65634707160368319999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.991 Γ— 10⁹⁴(95-digit number)
69913236870831371249…31269414320736639999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.398 Γ— 10⁹⁡(96-digit number)
13982647374166274249…62538828641473279999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.796 Γ— 10⁹⁡(96-digit number)
27965294748332548499…25077657282946559999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.593 Γ— 10⁹⁡(96-digit number)
55930589496665096999…50155314565893119999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.118 Γ— 10⁹⁢(97-digit number)
11186117899333019399…00310629131786239999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.237 Γ— 10⁹⁢(97-digit number)
22372235798666038799…00621258263572479999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.474 Γ— 10⁹⁢(97-digit number)
44744471597332077599…01242516527144959999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.948 Γ— 10⁹⁢(97-digit number)
89488943194664155199…02485033054289919999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.789 Γ— 10⁹⁷(98-digit number)
17897788638932831039…04970066108579839999
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 2649480

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 4083f0a6095b1b982a0622c2b28290737edce680e9f533afb8949e618ca9cade

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 #2,649,480 on Chainz β†—
Circulating Supply:57,910,037 XPMΒ·at block #6,833,230 Β· updates every 60s
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