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Home/Chain Registry/Block #2,748,010

Block #2,748,010

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2018, 2:40:25 AM Β· Difficulty 11.6511 Β· 4,095,086 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e8bf0c97c4461756e8e4ccd5a96768d4410adc24e20fd92f2371bf2880fd842d
View on Chainz β†—

Difficulty

11.651121

Transactions

1

Size

199 B

Version

2

Bits

0ba6afd6

Nonce

997,419,708

Timestamp

7/14/2018, 2:40:25 AM

Confirmations

4,095,086

Merkle Root

0ad2679477a05ef9f67747bd44f8a09f1382d5e22a5915fab2edb1d508bae2dc
Transactions (1)
Coinbase0ad2679477a05e…edb1d508bae2dc
1 in β†’ 1 out7.3500 XPM110 B
AXtQR5di…WP7g2JUs
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.

1.483 Γ— 10⁹³(94-digit number)
14830513703274592891…82827744083947158000
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.483 Γ— 10⁹³(94-digit number)
14830513703274592891…82827744083947157999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.966 Γ— 10⁹³(94-digit number)
29661027406549185783…65655488167894315999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.932 Γ— 10⁹³(94-digit number)
59322054813098371566…31310976335788631999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.186 Γ— 10⁹⁴(95-digit number)
11864410962619674313…62621952671577263999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.372 Γ— 10⁹⁴(95-digit number)
23728821925239348626…25243905343154527999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.745 Γ— 10⁹⁴(95-digit number)
47457643850478697253…50487810686309055999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.491 Γ— 10⁹⁴(95-digit number)
94915287700957394506…00975621372618111999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.898 Γ— 10⁹⁡(96-digit number)
18983057540191478901…01951242745236223999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.796 Γ— 10⁹⁡(96-digit number)
37966115080382957802…03902485490472447999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.593 Γ— 10⁹⁡(96-digit number)
75932230160765915605…07804970980944895999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.518 Γ— 10⁹⁢(97-digit number)
15186446032153183121…15609941961889791999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2748010

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 e8bf0c97c4461756e8e4ccd5a96768d4410adc24e20fd92f2371bf2880fd842d

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 #2,748,010 on Chainz β†—
Circulating Supply:57,989,130 XPMΒ·at block #6,843,095 Β· updates every 60s
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