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Block #3,276,901

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/22/2019, 10:32:24 AM Β· Difficulty 10.9950 Β· 3,568,715 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
806c6ba188c1b9e34c55180eb9c492ff9e0fd04668c7136c78f030f2349295f2
View on Chainz β†—

Difficulty

10.995034

Transactions

1

Size

200 B

Version

2

Bits

0afeba8d

Nonce

1,317,273,022

Timestamp

7/22/2019, 10:32:24 AM

Confirmations

3,568,715

Merkle Root

7f68245b2e965529ce88521cec8d95ec9d22e61d2c52c575f50d693844797e87
Transactions (1)
Coinbase7f68245b2e9655…0d693844797e87
1 in β†’ 1 out8.2600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

1.511 Γ— 10⁹⁴(95-digit number)
15111519079194605619…43931551465082122240
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
1.511 Γ— 10⁹⁴(95-digit number)
15111519079194605619…43931551465082122241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.022 Γ— 10⁹⁴(95-digit number)
30223038158389211238…87863102930164244481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.044 Γ— 10⁹⁴(95-digit number)
60446076316778422476…75726205860328488961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.208 Γ— 10⁹⁡(96-digit number)
12089215263355684495…51452411720656977921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.417 Γ— 10⁹⁡(96-digit number)
24178430526711368990…02904823441313955841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.835 Γ— 10⁹⁡(96-digit number)
48356861053422737980…05809646882627911681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.671 Γ— 10⁹⁡(96-digit number)
96713722106845475961…11619293765255823361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.934 Γ— 10⁹⁢(97-digit number)
19342744421369095192…23238587530511646721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.868 Γ— 10⁹⁢(97-digit number)
38685488842738190384…46477175061023293441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.737 Γ— 10⁹⁢(97-digit number)
77370977685476380769…92954350122046586881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.547 Γ— 10⁹⁷(98-digit number)
15474195537095276153…85908700244093173761
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 3276901

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 806c6ba188c1b9e34c55180eb9c492ff9e0fd04668c7136c78f030f2349295f2

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 #3,276,901 on Chainz β†—
Circulating Supply:58,009,374 XPMΒ·at block #6,845,615 Β· updates every 60s
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