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Home/Chain Registry/Block #2,829,301

Block #2,829,301

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/7/2018, 9:56:36 PM Β· Difficulty 11.7126 Β· 4,012,973 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f0480b538191fb3e8798ae6f9dd5659ed5867370042ca2353ad50a84ad042f80
View on Chainz β†—

Difficulty

11.712643

Transactions

1

Size

201 B

Version

2

Bits

0bb66fc5

Nonce

1,511,398,884

Timestamp

9/7/2018, 9:56:36 PM

Confirmations

4,012,973

Merkle Root

03f17183309df12e321e3d1b5f62aaccdc814b7e30986625bcdeb10c9f5686e6
Transactions (1)
Coinbase03f17183309df1…deb10c9f5686e6
1 in β†’ 1 out7.2800 XPM110 B
AJoQ1zdR…Y2Yx5k24
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.

1.815 Γ— 10⁹⁷(98-digit number)
18159885838073518233…63917350517279390720
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
1.815 Γ— 10⁹⁷(98-digit number)
18159885838073518233…63917350517279390719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.631 Γ— 10⁹⁷(98-digit number)
36319771676147036467…27834701034558781439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.263 Γ— 10⁹⁷(98-digit number)
72639543352294072935…55669402069117562879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.452 Γ— 10⁹⁸(99-digit number)
14527908670458814587…11338804138235125759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.905 Γ— 10⁹⁸(99-digit number)
29055817340917629174…22677608276470251519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.811 Γ— 10⁹⁸(99-digit number)
58111634681835258348…45355216552940503039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.162 Γ— 10⁹⁹(100-digit number)
11622326936367051669…90710433105881006079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.324 Γ— 10⁹⁹(100-digit number)
23244653872734103339…81420866211762012159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.648 Γ— 10⁹⁹(100-digit number)
46489307745468206678…62841732423524024319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.297 Γ— 10⁹⁹(100-digit number)
92978615490936413357…25683464847048048639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.859 Γ— 10¹⁰⁰(101-digit number)
18595723098187282671…51366929694096097279
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 2829301

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 f0480b538191fb3e8798ae6f9dd5659ed5867370042ca2353ad50a84ad042f80

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 #2,829,301 on Chainz β†—
Circulating Supply:57,982,593 XPMΒ·at block #6,842,273 Β· updates every 60s
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