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Home/Chain Registry/Block #2,775,786

Block #2,775,786

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/2/2018, 7:49:52 AM Β· Difficulty 11.6594 Β· 4,061,119 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f4a6663b79f0f40e184f36c680c2beaa62f904aff022ee6dc4f4b558b0a1d7e1
View on Chainz β†—

Difficulty

11.659387

Transactions

2

Size

539 B

Version

2

Bits

0ba8cd99

Nonce

953,132,702

Timestamp

8/2/2018, 7:49:52 AM

Confirmations

4,061,119

Merkle Root

0d7211b3453b03ae01d17b6c71183441641fad5ccf6ea5fbc952f9a4b6fb5aa5
Transactions (2)
Coinbase47739b0282cbd9…ddab31055de146
1 in β†’ 1 out7.3500 XPM110 B
AHzgXNAF…SS4RE7j8
0ab13055b0f213…d532ea63f95e72
2 in β†’ 2 out12.0400 XPM339 B
AemXjBq4…CU7GYfZYAWTAGcL4…jKZwu5r5
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.

4.964 Γ— 10⁹⁡(96-digit number)
49645044127371523091…88258822458871568640
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
4.964 Γ— 10⁹⁡(96-digit number)
49645044127371523091…88258822458871568641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.929 Γ— 10⁹⁡(96-digit number)
99290088254743046183…76517644917743137281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.985 Γ— 10⁹⁢(97-digit number)
19858017650948609236…53035289835486274561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.971 Γ— 10⁹⁢(97-digit number)
39716035301897218473…06070579670972549121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.943 Γ— 10⁹⁢(97-digit number)
79432070603794436946…12141159341945098241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.588 Γ— 10⁹⁷(98-digit number)
15886414120758887389…24282318683890196481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.177 Γ— 10⁹⁷(98-digit number)
31772828241517774778…48564637367780392961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.354 Γ— 10⁹⁷(98-digit number)
63545656483035549557…97129274735560785921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.270 Γ— 10⁹⁸(99-digit number)
12709131296607109911…94258549471121571841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.541 Γ— 10⁹⁸(99-digit number)
25418262593214219822…88517098942243143681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.083 Γ— 10⁹⁸(99-digit number)
50836525186428439645…77034197884486287361
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 2775786

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 f4a6663b79f0f40e184f36c680c2beaa62f904aff022ee6dc4f4b558b0a1d7e1

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 #2,775,786 on Chainz β†—
Circulating Supply:57,939,532 XPMΒ·at block #6,836,904 Β· updates every 60s
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