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Home/Chain Registry/Block #2,647,754

Block #2,647,754

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/4/2018, 2:40:14 AM Β· Difficulty 11.7622 Β· 4,185,669 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b11942a510d7c8999615b5e99f4541f4b9c4543850f6a3a5a99de3f2466322da
View on Chainz β†—

Difficulty

11.762230

Transactions

2

Size

20.80 KB

Version

2

Bits

0bc32185

Nonce

2,027,573,069

Timestamp

5/4/2018, 2:40:14 AM

Confirmations

4,185,669

Merkle Root

d459a3fac7cc1fb56db674ee1e66f1936302ff57e63ff2862bd0bc09a78b032b
Transactions (2)
Coinbase4e82e6b392eddc…d5c848d8b423cc
1 in β†’ 1 out7.4400 XPM110 B
APxCeVwU…3Y8jRthg
589a0a6215c970…4d79f206262e6d
142 in β†’ 2 out562.7800 XPM20.60 KB
AXGXMsf4…GvhPMde2AZ3QSf7f…zd1mV8bu
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.

1.031 Γ— 10⁹⁴(95-digit number)
10313174729213664119…87161551719871460480
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
1.031 Γ— 10⁹⁴(95-digit number)
10313174729213664119…87161551719871460481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.062 Γ— 10⁹⁴(95-digit number)
20626349458427328238…74323103439742920961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.125 Γ— 10⁹⁴(95-digit number)
41252698916854656476…48646206879485841921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.250 Γ— 10⁹⁴(95-digit number)
82505397833709312952…97292413758971683841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.650 Γ— 10⁹⁡(96-digit number)
16501079566741862590…94584827517943367681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.300 Γ— 10⁹⁡(96-digit number)
33002159133483725181…89169655035886735361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.600 Γ— 10⁹⁡(96-digit number)
66004318266967450362…78339310071773470721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.320 Γ— 10⁹⁢(97-digit number)
13200863653393490072…56678620143546941441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.640 Γ— 10⁹⁢(97-digit number)
26401727306786980144…13357240287093882881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.280 Γ— 10⁹⁢(97-digit number)
52803454613573960289…26714480574187765761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.056 Γ— 10⁹⁷(98-digit number)
10560690922714792057…53428961148375531521
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 2647754

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 b11942a510d7c8999615b5e99f4541f4b9c4543850f6a3a5a99de3f2466322da

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 #2,647,754 on Chainz β†—
Circulating Supply:57,911,588 XPMΒ·at block #6,833,422 Β· updates every 60s
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