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Block #2,291,620

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/11/2017, 5:12:26 AM Β· Difficulty 10.9550 Β· 4,550,601 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
46da922fd35f5050be529d2c6558db8537b0b546bf55491214e9eb760be4bde2
View on Chainz β†—

Difficulty

10.955009

Transactions

1

Size

200 B

Version

2

Bits

0af47b80

Nonce

785,789,340

Timestamp

9/11/2017, 5:12:26 AM

Confirmations

4,550,601

Merkle Root

6d8682fb3128669d832d5d003a5f079bcd38f5b7a4184183acffe28bde2f403f
Transactions (1)
Coinbase6d8682fb312866…ffe28bde2f403f
1 in β†’ 1 out8.3200 XPM110 B
AN2nrjVG…X4shpeYT
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.

4.602 Γ— 10⁹³(94-digit number)
46028736372673733860…82595223300952251200
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
4.602 Γ— 10⁹³(94-digit number)
46028736372673733860…82595223300952251199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.205 Γ— 10⁹³(94-digit number)
92057472745347467721…65190446601904502399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.841 Γ— 10⁹⁴(95-digit number)
18411494549069493544…30380893203809004799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.682 Γ— 10⁹⁴(95-digit number)
36822989098138987088…60761786407618009599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.364 Γ— 10⁹⁴(95-digit number)
73645978196277974177…21523572815236019199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.472 Γ— 10⁹⁡(96-digit number)
14729195639255594835…43047145630472038399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.945 Γ— 10⁹⁡(96-digit number)
29458391278511189670…86094291260944076799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.891 Γ— 10⁹⁡(96-digit number)
58916782557022379341…72188582521888153599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.178 Γ— 10⁹⁢(97-digit number)
11783356511404475868…44377165043776307199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.356 Γ— 10⁹⁢(97-digit number)
23566713022808951736…88754330087552614399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.713 Γ— 10⁹⁢(97-digit number)
47133426045617903473…77508660175105228799
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 2291620

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 46da922fd35f5050be529d2c6558db8537b0b546bf55491214e9eb760be4bde2

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 #2,291,620 on Chainz β†—
Circulating Supply:57,982,166 XPMΒ·at block #6,842,220 Β· updates every 60s
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