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Home/Chain Registry/Block #2,145,172

Block #2,145,172

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/4/2017, 11:03:17 AM Β· Difficulty 10.8872 Β· 4,679,663 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ac989a05d5e0e3d4cdee3d4d3d4f937adc03ec8bf4ab8dd6d79570ecae01f054
View on Chainz β†—

Difficulty

10.887169

Transactions

1

Size

200 B

Version

2

Bits

0ae31d85

Nonce

64,115,601

Timestamp

6/4/2017, 11:03:17 AM

Confirmations

4,679,663

Merkle Root

c4f861193487c23565a7c9126aecbe16b1b935424085b174542571f2aec62d53
Transactions (1)
Coinbasec4f861193487c2…2571f2aec62d53
1 in β†’ 1 out8.4200 XPM110 B
AVFkVK4K…mAKn2zL5
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.

5.333 Γ— 10⁹⁴(95-digit number)
53332595085464547372…22925272908593745640
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
5.333 Γ— 10⁹⁴(95-digit number)
53332595085464547372…22925272908593745641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.066 Γ— 10⁹⁡(96-digit number)
10666519017092909474…45850545817187491281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.133 Γ— 10⁹⁡(96-digit number)
21333038034185818948…91701091634374982561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.266 Γ— 10⁹⁡(96-digit number)
42666076068371637897…83402183268749965121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.533 Γ— 10⁹⁡(96-digit number)
85332152136743275795…66804366537499930241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.706 Γ— 10⁹⁢(97-digit number)
17066430427348655159…33608733074999860481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.413 Γ— 10⁹⁢(97-digit number)
34132860854697310318…67217466149999720961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.826 Γ— 10⁹⁢(97-digit number)
68265721709394620636…34434932299999441921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.365 Γ— 10⁹⁷(98-digit number)
13653144341878924127…68869864599998883841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.730 Γ— 10⁹⁷(98-digit number)
27306288683757848254…37739729199997767681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.461 Γ— 10⁹⁷(98-digit number)
54612577367515696509…75479458399995535361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second 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
RareChain length 11
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2145172

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 ac989a05d5e0e3d4cdee3d4d3d4f937adc03ec8bf4ab8dd6d79570ecae01f054

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 #2,145,172 on Chainz β†—
Circulating Supply:57,842,760 XPMΒ·at block #6,824,834 Β· updates every 60s
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