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Home/Chain Registry/Block #2,169,159

Block #2,169,159

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/20/2017, 6:13:18 PM Β· Difficulty 10.8989 Β· 4,670,276 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8093d0fd32d483b12db46c8b2ae356d0adb419d9cc2979b51742e5dd467b3e1e
View on Chainz β†—

Difficulty

10.898925

Transactions

1

Size

200 B

Version

2

Bits

0ae61fef

Nonce

866,547,001

Timestamp

6/20/2017, 6:13:18 PM

Confirmations

4,670,276

Merkle Root

0130954656d5583e01a1d5b9d91bfdd4a536b5f22e07b0116719b1c8c6abdf70
Transactions (1)
Coinbase0130954656d558…19b1c8c6abdf70
1 in β†’ 1 out8.4100 XPM110 B
AQPx834q…xg3j8MH9
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.

5.409 Γ— 10⁹⁴(95-digit number)
54097826553235316710…04490990662665361760
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
5.409 Γ— 10⁹⁴(95-digit number)
54097826553235316710…04490990662665361759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.081 Γ— 10⁹⁡(96-digit number)
10819565310647063342…08981981325330723519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.163 Γ— 10⁹⁡(96-digit number)
21639130621294126684…17963962650661447039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.327 Γ— 10⁹⁡(96-digit number)
43278261242588253368…35927925301322894079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.655 Γ— 10⁹⁡(96-digit number)
86556522485176506736…71855850602645788159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.731 Γ— 10⁹⁢(97-digit number)
17311304497035301347…43711701205291576319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.462 Γ— 10⁹⁢(97-digit number)
34622608994070602694…87423402410583152639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.924 Γ— 10⁹⁢(97-digit number)
69245217988141205389…74846804821166305279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.384 Γ— 10⁹⁷(98-digit number)
13849043597628241077…49693609642332610559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.769 Γ— 10⁹⁷(98-digit number)
27698087195256482155…99387219284665221119
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 2169159

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 8093d0fd32d483b12db46c8b2ae356d0adb419d9cc2979b51742e5dd467b3e1e

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 #2,169,159 on Chainz β†—
Circulating Supply:57,959,767 XPMΒ·at block #6,839,434 Β· updates every 60s
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