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Home/Chain Registry/Block #2,164,102

Block #2,164,102

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/17/2017, 5:34:33 AM Β· Difficulty 10.8992 Β· 4,660,578 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
33defe2155da283c8a49c7f4f38c999b2f4ea4ce0fbb93198e657db5c7a78c7c
View on Chainz β†—

Difficulty

10.899201

Transactions

1

Size

199 B

Version

2

Bits

0ae6320e

Nonce

192,999,105

Timestamp

6/17/2017, 5:34:33 AM

Confirmations

4,660,578

Merkle Root

0647082d000f1ec52917f7cd910acc7cfee8f7e97aa17c2027e6e4bcb7841d9a
Transactions (1)
Coinbase0647082d000f1e…e6e4bcb7841d9a
1 in β†’ 1 out8.4000 XPM109 B
ARq6W2t7…gcCURzdM
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.

8.872 Γ— 10⁹⁡(96-digit number)
88724799568292185066…71118266548615401600
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
8.872 Γ— 10⁹⁡(96-digit number)
88724799568292185066…71118266548615401599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.774 Γ— 10⁹⁢(97-digit number)
17744959913658437013…42236533097230803199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.548 Γ— 10⁹⁢(97-digit number)
35489919827316874026…84473066194461606399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.097 Γ— 10⁹⁢(97-digit number)
70979839654633748053…68946132388923212799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.419 Γ— 10⁹⁷(98-digit number)
14195967930926749610…37892264777846425599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.839 Γ— 10⁹⁷(98-digit number)
28391935861853499221…75784529555692851199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.678 Γ— 10⁹⁷(98-digit number)
56783871723706998442…51569059111385702399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.135 Γ— 10⁹⁸(99-digit number)
11356774344741399688…03138118222771404799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.271 Γ— 10⁹⁸(99-digit number)
22713548689482799377…06276236445542809599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.542 Γ— 10⁹⁸(99-digit number)
45427097378965598754…12552472891085619199
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 2164102

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 33defe2155da283c8a49c7f4f38c999b2f4ea4ce0fbb93198e657db5c7a78c7c

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 #2,164,102 on Chainz β†—
Circulating Supply:57,841,505 XPMΒ·at block #6,824,679 Β· updates every 60s
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