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Home/Chain Registry/Block #2,176,085

Block #2,176,085

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/24/2017, 8:07:29 PM Β· Difficulty 10.9182 Β· 4,666,122 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
68f98ced61234d28fc3f1c5de5dfd7e8abd887736e3aa94921da35db38b6b6f9
View on Chainz β†—

Difficulty

10.918150

Transactions

1

Size

199 B

Version

2

Bits

0aeb0be8

Nonce

580,214,286

Timestamp

6/24/2017, 8:07:29 PM

Confirmations

4,666,122

Merkle Root

a7f8e1a8ee5461006ed0ae347045bd9a84601e601258f25e68b65e043a815753
Transactions (1)
Coinbasea7f8e1a8ee5461…b65e043a815753
1 in β†’ 1 out8.3800 XPM110 B
AHvEKsm9…MBfTscn4
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.

1.378 Γ— 10⁹³(94-digit number)
13780724247477770486…77430149782294519040
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
1.378 Γ— 10⁹³(94-digit number)
13780724247477770486…77430149782294519039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.756 Γ— 10⁹³(94-digit number)
27561448494955540972…54860299564589038079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.512 Γ— 10⁹³(94-digit number)
55122896989911081944…09720599129178076159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.102 Γ— 10⁹⁴(95-digit number)
11024579397982216388…19441198258356152319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.204 Γ— 10⁹⁴(95-digit number)
22049158795964432777…38882396516712304639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.409 Γ— 10⁹⁴(95-digit number)
44098317591928865555…77764793033424609279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.819 Γ— 10⁹⁴(95-digit number)
88196635183857731111…55529586066849218559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.763 Γ— 10⁹⁡(96-digit number)
17639327036771546222…11059172133698437119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.527 Γ— 10⁹⁡(96-digit number)
35278654073543092444…22118344267396874239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.055 Γ— 10⁹⁡(96-digit number)
70557308147086184888…44236688534793748479
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 2176085

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 68f98ced61234d28fc3f1c5de5dfd7e8abd887736e3aa94921da35db38b6b6f9

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 #2,176,085 on Chainz β†—
Circulating Supply:57,982,052 XPMΒ·at block #6,842,206 Β· updates every 60s
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