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Home/Chain Registry/Block #2,576,116

Block #2,576,116

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/20/2018, 4:06:29 PM Β· Difficulty 10.9956 Β· 4,266,654 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dfab865a7a9b77eac35f14ae6c2e64bbf61a9a3b2f77fa6115cedbdcbd59e1da
View on Chainz β†—

Difficulty

10.995647

Transactions

1

Size

201 B

Version

2

Bits

0afee2c1

Nonce

201,901,202

Timestamp

3/20/2018, 4:06:29 PM

Confirmations

4,266,654

Merkle Root

a72c0af8ce495bf9f5365926a14d403f20ff7b5ccf6a04929854be872d36107f
Transactions (1)
Coinbasea72c0af8ce495b…54be872d36107f
1 in β†’ 1 out8.2600 XPM110 B
Acj3xEdW…JHb29M43
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.

3.412 Γ— 10⁹⁢(97-digit number)
34129695642971815143…35874848737186846720
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
3.412 Γ— 10⁹⁢(97-digit number)
34129695642971815143…35874848737186846721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.825 Γ— 10⁹⁢(97-digit number)
68259391285943630287…71749697474373693441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.365 Γ— 10⁹⁷(98-digit number)
13651878257188726057…43499394948747386881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.730 Γ— 10⁹⁷(98-digit number)
27303756514377452114…86998789897494773761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.460 Γ— 10⁹⁷(98-digit number)
54607513028754904229…73997579794989547521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.092 Γ— 10⁹⁸(99-digit number)
10921502605750980845…47995159589979095041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.184 Γ— 10⁹⁸(99-digit number)
21843005211501961691…95990319179958190081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.368 Γ— 10⁹⁸(99-digit number)
43686010423003923383…91980638359916380161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.737 Γ— 10⁹⁸(99-digit number)
87372020846007846767…83961276719832760321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.747 Γ— 10⁹⁹(100-digit number)
17474404169201569353…67922553439665520641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.494 Γ— 10⁹⁹(100-digit number)
34948808338403138707…35845106879331041281
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 2576116

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 dfab865a7a9b77eac35f14ae6c2e64bbf61a9a3b2f77fa6115cedbdcbd59e1da

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 #2,576,116 on Chainz β†—
Circulating Supply:57,986,498 XPMΒ·at block #6,842,769 Β· updates every 60s
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