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Home/Chain Registry/Block #2,827,860

Block #2,827,860

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/6/2018, 10:13:42 PM Β· Difficulty 11.7116 Β· 4,016,180 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
67e79d20190d3f80febd61baa4dd69ff3b1ff443cf8d76500f92bf4bd30e5fc1
View on Chainz β†—

Difficulty

11.711552

Transactions

1

Size

200 B

Version

2

Bits

0bb62849

Nonce

1,974,506,487

Timestamp

9/6/2018, 10:13:42 PM

Confirmations

4,016,180

Merkle Root

7fd6080deb052e18cf948abda7d73cb8e89464ea5d0a7396171f5b64e9010ca6
Transactions (1)
Coinbase7fd6080deb052e…1f5b64e9010ca6
1 in β†’ 1 out7.2800 XPM110 B
AQ4bDtqv…ShuKXpwt
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.

1.855 Γ— 10⁹⁴(95-digit number)
18558612719860594874…41470986909397402720
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
1.855 Γ— 10⁹⁴(95-digit number)
18558612719860594874…41470986909397402721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.711 Γ— 10⁹⁴(95-digit number)
37117225439721189749…82941973818794805441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.423 Γ— 10⁹⁴(95-digit number)
74234450879442379499…65883947637589610881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.484 Γ— 10⁹⁡(96-digit number)
14846890175888475899…31767895275179221761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.969 Γ— 10⁹⁡(96-digit number)
29693780351776951799…63535790550358443521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.938 Γ— 10⁹⁡(96-digit number)
59387560703553903599…27071581100716887041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.187 Γ— 10⁹⁢(97-digit number)
11877512140710780719…54143162201433774081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.375 Γ— 10⁹⁢(97-digit number)
23755024281421561439…08286324402867548161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.751 Γ— 10⁹⁢(97-digit number)
47510048562843122879…16572648805735096321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.502 Γ— 10⁹⁢(97-digit number)
95020097125686245759…33145297611470192641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.900 Γ— 10⁹⁷(98-digit number)
19004019425137249151…66290595222940385281
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 2827860

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 67e79d20190d3f80febd61baa4dd69ff3b1ff443cf8d76500f92bf4bd30e5fc1

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 #2,827,860 on Chainz β†—
Circulating Supply:57,996,689 XPMΒ·at block #6,844,039 Β· updates every 60s
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