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Home/Chain Registry/Block #2,102,752

Block #2,102,752

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/6/2017, 10:13:56 AM Β· Difficulty 10.8709 Β· 4,740,474 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
75d1922c281a87bfafdb310ecce431c053e0e9e423c5f4865cc25d1bffa8b883
View on Chainz β†—

Difficulty

10.870925

Transactions

1

Size

199 B

Version

2

Bits

0adef4f1

Nonce

428,352,039

Timestamp

5/6/2017, 10:13:56 AM

Confirmations

4,740,474

Merkle Root

10db7656831bd7a0980b0e616db74f4408026ad631c545e10197ada46424ea0a
Transactions (1)
Coinbase10db7656831bd7…97ada46424ea0a
1 in β†’ 1 out8.4500 XPM109 B
Aa7Dg2Z3…bGbgEVuF
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.

1.504 Γ— 10⁹⁡(96-digit number)
15047882061187804455…64270674369380608000
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
1.504 Γ— 10⁹⁡(96-digit number)
15047882061187804455…64270674369380607999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.009 Γ— 10⁹⁡(96-digit number)
30095764122375608910…28541348738761215999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.019 Γ— 10⁹⁡(96-digit number)
60191528244751217820…57082697477522431999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.203 Γ— 10⁹⁢(97-digit number)
12038305648950243564…14165394955044863999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.407 Γ— 10⁹⁢(97-digit number)
24076611297900487128…28330789910089727999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.815 Γ— 10⁹⁢(97-digit number)
48153222595800974256…56661579820179455999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.630 Γ— 10⁹⁢(97-digit number)
96306445191601948512…13323159640358911999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.926 Γ— 10⁹⁷(98-digit number)
19261289038320389702…26646319280717823999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.852 Γ— 10⁹⁷(98-digit number)
38522578076640779404…53292638561435647999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.704 Γ— 10⁹⁷(98-digit number)
77045156153281558809…06585277122871295999
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 2102752

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 75d1922c281a87bfafdb310ecce431c053e0e9e423c5f4865cc25d1bffa8b883

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 #2,102,752 on Chainz β†—
Circulating Supply:57,990,182 XPMΒ·at block #6,843,225 Β· updates every 60s
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