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Home/Chain Registry/Block #2,311,796

Block #2,311,796

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/27/2017, 8:01:21 PM Β· Difficulty 10.9062 Β· 4,531,990 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2975b821fc8538baf77984b738b849c480a4e4e307f0f7fdf7354f3466a06584
View on Chainz β†—

Difficulty

10.906193

Transactions

1

Size

200 B

Version

2

Bits

0ae7fc40

Nonce

1,494,009,896

Timestamp

9/27/2017, 8:01:21 PM

Confirmations

4,531,990

Merkle Root

a4e833ec2c927a8ba213b58b32be438857aa31e8e35dec5ae5b19d4972add4b0
Transactions (1)
Coinbasea4e833ec2c927a…b19d4972add4b0
1 in β†’ 1 out8.3900 XPM110 B
AUqVWCqJ…EXgx4cK7
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.

2.029 Γ— 10⁹⁡(96-digit number)
20297185622474800877…37696072001178481280
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
2.029 Γ— 10⁹⁡(96-digit number)
20297185622474800877…37696072001178481279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.059 Γ— 10⁹⁡(96-digit number)
40594371244949601754…75392144002356962559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.118 Γ— 10⁹⁡(96-digit number)
81188742489899203508…50784288004713925119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.623 Γ— 10⁹⁢(97-digit number)
16237748497979840701…01568576009427850239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.247 Γ— 10⁹⁢(97-digit number)
32475496995959681403…03137152018855700479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.495 Γ— 10⁹⁢(97-digit number)
64950993991919362806…06274304037711400959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.299 Γ— 10⁹⁷(98-digit number)
12990198798383872561…12548608075422801919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.598 Γ— 10⁹⁷(98-digit number)
25980397596767745122…25097216150845603839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.196 Γ— 10⁹⁷(98-digit number)
51960795193535490245…50194432301691207679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.039 Γ— 10⁹⁸(99-digit number)
10392159038707098049…00388864603382415359
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 2311796

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 2975b821fc8538baf77984b738b849c480a4e4e307f0f7fdf7354f3466a06584

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 #2,311,796 on Chainz β†—
Circulating Supply:57,994,664 XPMΒ·at block #6,843,785 Β· updates every 60s
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