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Home/Chain Registry/Block #2,753,143

Block #2,753,143

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/17/2018, 3:44:00 PM Β· Difficulty 11.6533 Β· 4,088,881 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
48e87ff38eee0a0fa74d9426959716987914964c825860d8dd209fbe029c5271
View on Chainz β†—

Difficulty

11.653258

Transactions

1

Size

200 B

Version

2

Bits

0ba73bea

Nonce

506,111,744

Timestamp

7/17/2018, 3:44:00 PM

Confirmations

4,088,881

Merkle Root

3287a7c158fe3674ed56c911fe44fc56d773795216ea09576ec8786bf0627342
Transactions (1)
Coinbase3287a7c158fe36…c8786bf0627342
1 in β†’ 1 out7.3500 XPM110 B
AV1Avwvo…t4RU6FYa
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.

3.000 Γ— 10⁹⁴(95-digit number)
30004262677417390063…44048383569358479280
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
3.000 Γ— 10⁹⁴(95-digit number)
30004262677417390063…44048383569358479281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.000 Γ— 10⁹⁴(95-digit number)
60008525354834780126…88096767138716958561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.200 Γ— 10⁹⁡(96-digit number)
12001705070966956025…76193534277433917121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.400 Γ— 10⁹⁡(96-digit number)
24003410141933912050…52387068554867834241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.800 Γ— 10⁹⁡(96-digit number)
48006820283867824101…04774137109735668481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.601 Γ— 10⁹⁡(96-digit number)
96013640567735648202…09548274219471336961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.920 Γ— 10⁹⁢(97-digit number)
19202728113547129640…19096548438942673921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.840 Γ— 10⁹⁢(97-digit number)
38405456227094259280…38193096877885347841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.681 Γ— 10⁹⁢(97-digit number)
76810912454188518561…76386193755770695681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.536 Γ— 10⁹⁷(98-digit number)
15362182490837703712…52772387511541391361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.072 Γ— 10⁹⁷(98-digit number)
30724364981675407424…05544775023082782721
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 2753143

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 48e87ff38eee0a0fa74d9426959716987914964c825860d8dd209fbe029c5271

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 #2,753,143 on Chainz β†—
Circulating Supply:57,980,578 XPMΒ·at block #6,842,023 Β· updates every 60s
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