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Home/Chain Registry/Block #2,762,091

Block #2,762,091

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/23/2018, 8:32:00 PM Β· Difficulty 11.6550 Β· 4,038,486 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5dde94fb7809a5417d5e593a1e9acf66fa4086213ec382cd751a301ea59be55c
View on Chainz β†—

Difficulty

11.655044

Transactions

1

Size

200 B

Version

2

Bits

0ba7b0f0

Nonce

1,332,431,769

Timestamp

7/23/2018, 8:32:00 PM

Confirmations

4,038,486

Merkle Root

1612377bf1cf13a6e962f27a299953507d71037a2f5f1fc880d4814b700c1047
Transactions (1)
Coinbase1612377bf1cf13…d4814b700c1047
1 in β†’ 1 out7.3500 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.

5.455 Γ— 10⁹⁴(95-digit number)
54556305622999614775…44769429403739199350
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
5.455 Γ— 10⁹⁴(95-digit number)
54556305622999614775…44769429403739199349
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.091 Γ— 10⁹⁡(96-digit number)
10911261124599922955…89538858807478398699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.182 Γ— 10⁹⁡(96-digit number)
21822522249199845910…79077717614956797399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.364 Γ— 10⁹⁡(96-digit number)
43645044498399691820…58155435229913594799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.729 Γ— 10⁹⁡(96-digit number)
87290088996799383640…16310870459827189599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.745 Γ— 10⁹⁢(97-digit number)
17458017799359876728…32621740919654379199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.491 Γ— 10⁹⁢(97-digit number)
34916035598719753456…65243481839308758399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.983 Γ— 10⁹⁢(97-digit number)
69832071197439506912…30486963678617516799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.396 Γ— 10⁹⁷(98-digit number)
13966414239487901382…60973927357235033599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.793 Γ— 10⁹⁷(98-digit number)
27932828478975802764…21947854714470067199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.586 Γ— 10⁹⁷(98-digit number)
55865656957951605529…43895709428940134399
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 2762091

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 5dde94fb7809a5417d5e593a1e9acf66fa4086213ec382cd751a301ea59be55c

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 #2,762,091 on Chainz β†—
Circulating Supply:57,648,672 XPMΒ·at block #6,800,576 Β· updates every 60s
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