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Home/Chain Registry/Block #2,731,326

Block #2,731,326

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/2/2018, 5:05:25 PM Β· Difficulty 11.6313 Β· 4,114,323 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
59f37ed055cbc6e1241a2c9328aa4f28a88fa23241f54843538ac00585bf8cae
View on Chainz β†—

Difficulty

11.631332

Transactions

1

Size

199 B

Version

2

Bits

0ba19ef8

Nonce

647,438

Timestamp

7/2/2018, 5:05:25 PM

Confirmations

4,114,323

Merkle Root

d5a0dd966a0ca3dd13332721f8a3c290382a6e3f15e7c989ff272602eac76cf9
Transactions (1)
Coinbased5a0dd966a0ca3…272602eac76cf9
1 in β†’ 1 out7.3800 XPM110 B
AZtxQr2F…7grUWrUz
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.

1.957 Γ— 10⁹³(94-digit number)
19570244403557605640…35542139639661772800
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
1.957 Γ— 10⁹³(94-digit number)
19570244403557605640…35542139639661772801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.914 Γ— 10⁹³(94-digit number)
39140488807115211280…71084279279323545601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.828 Γ— 10⁹³(94-digit number)
78280977614230422560…42168558558647091201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.565 Γ— 10⁹⁴(95-digit number)
15656195522846084512…84337117117294182401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.131 Γ— 10⁹⁴(95-digit number)
31312391045692169024…68674234234588364801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.262 Γ— 10⁹⁴(95-digit number)
62624782091384338048…37348468469176729601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.252 Γ— 10⁹⁡(96-digit number)
12524956418276867609…74696936938353459201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.504 Γ— 10⁹⁡(96-digit number)
25049912836553735219…49393873876706918401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.009 Γ— 10⁹⁡(96-digit number)
50099825673107470438…98787747753413836801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.001 Γ— 10⁹⁢(97-digit number)
10019965134621494087…97575495506827673601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.003 Γ— 10⁹⁢(97-digit number)
20039930269242988175…95150991013655347201
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 2731326

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 59f37ed055cbc6e1241a2c9328aa4f28a88fa23241f54843538ac00585bf8cae

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 #2,731,326 on Chainz β†—
Circulating Supply:58,009,641 XPMΒ·at block #6,845,648 Β· updates every 60s
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