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Home/Chain Registry/Block #2,949,170

Block #2,949,170

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/2/2018, 6:46:20 PM Β· Difficulty 11.3984 Β· 3,887,501 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
91efd3fe4cd424cd8fc81b32612711783b6a5c62208be716764c08aa2cb1ee50
View on Chainz β†—

Difficulty

11.398398

Transactions

1

Size

200 B

Version

2

Bits

0b65fd69

Nonce

246,333,967

Timestamp

12/2/2018, 6:46:20 PM

Confirmations

3,887,501

Merkle Root

f5402ef336cf9c14033282d96d975dcb11e4e1f98ab7dc8e3da5b2b5d3dce33f
Transactions (1)
Coinbasef5402ef336cf9c…a5b2b5d3dce33f
1 in β†’ 1 out7.6800 XPM110 B
AUMQRepm…tAfKmdW1
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.

6.455 Γ— 10⁹⁴(95-digit number)
64558096723073312276…88650991769480185600
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
6.455 Γ— 10⁹⁴(95-digit number)
64558096723073312276…88650991769480185601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.291 Γ— 10⁹⁡(96-digit number)
12911619344614662455…77301983538960371201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.582 Γ— 10⁹⁡(96-digit number)
25823238689229324910…54603967077920742401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.164 Γ— 10⁹⁡(96-digit number)
51646477378458649821…09207934155841484801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.032 Γ— 10⁹⁢(97-digit number)
10329295475691729964…18415868311682969601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.065 Γ— 10⁹⁢(97-digit number)
20658590951383459928…36831736623365939201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.131 Γ— 10⁹⁢(97-digit number)
41317181902766919857…73663473246731878401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.263 Γ— 10⁹⁢(97-digit number)
82634363805533839714…47326946493463756801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.652 Γ— 10⁹⁷(98-digit number)
16526872761106767942…94653892986927513601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.305 Γ— 10⁹⁷(98-digit number)
33053745522213535885…89307785973855027201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.610 Γ— 10⁹⁷(98-digit number)
66107491044427071771…78615571947710054401
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 2949170

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 91efd3fe4cd424cd8fc81b32612711783b6a5c62208be716764c08aa2cb1ee50

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 #2,949,170 on Chainz β†—
Circulating Supply:57,937,647 XPMΒ·at block #6,836,670 Β· updates every 60s
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