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Block #2,730,860

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/2/2018, 9:25:47 AM Β· Difficulty 11.6309 Β· 4,112,601 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dca7453851ca5a0ecab421212aa9d48417d37b351450751c67d3ee93fd54a8b1
View on Chainz β†—

Difficulty

11.630903

Transactions

1

Size

199 B

Version

2

Bits

0ba182e1

Nonce

1,432,526,993

Timestamp

7/2/2018, 9:25:47 AM

Confirmations

4,112,601

Merkle Root

3066913b9e12421a2e71031224dee3b3ee3726ab89b0c959aad4fc63a548098f
Transactions (1)
Coinbase3066913b9e1242…d4fc63a548098f
1 in β†’ 1 out7.3800 XPM109 B
ALQGpaT6…9dLVU1B9
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.

9.978 Γ— 10⁹⁴(95-digit number)
99784039909210878307…86047516723526035200
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
9.978 Γ— 10⁹⁴(95-digit number)
99784039909210878307…86047516723526035201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.995 Γ— 10⁹⁡(96-digit number)
19956807981842175661…72095033447052070401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.991 Γ— 10⁹⁡(96-digit number)
39913615963684351322…44190066894104140801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.982 Γ— 10⁹⁡(96-digit number)
79827231927368702645…88380133788208281601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.596 Γ— 10⁹⁢(97-digit number)
15965446385473740529…76760267576416563201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.193 Γ— 10⁹⁢(97-digit number)
31930892770947481058…53520535152833126401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.386 Γ— 10⁹⁢(97-digit number)
63861785541894962116…07041070305666252801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.277 Γ— 10⁹⁷(98-digit number)
12772357108378992423…14082140611332505601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.554 Γ— 10⁹⁷(98-digit number)
25544714216757984846…28164281222665011201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.108 Γ— 10⁹⁷(98-digit number)
51089428433515969693…56328562445330022401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.021 Γ— 10⁹⁸(99-digit number)
10217885686703193938…12657124890660044801
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 2730860

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 dca7453851ca5a0ecab421212aa9d48417d37b351450751c67d3ee93fd54a8b1

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 #2,730,860 on Chainz β†—
Circulating Supply:57,992,057 XPMΒ·at block #6,843,460 Β· updates every 60s
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