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Home/Chain Registry/Block #2,650,864

Block #2,650,864

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/6/2018, 9:27:03 AM Β· Difficulty 11.7538 Β· 4,182,132 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b916f4b34babedaa2781c4e2013665cd70bdcef99e8d871620d49ec199c20fd4
View on Chainz β†—

Difficulty

11.753813

Transactions

2

Size

720 B

Version

2

Bits

0bc0f9e6

Nonce

187,853,442

Timestamp

5/6/2018, 9:27:03 AM

Confirmations

4,182,132

Merkle Root

19e83f6d9f6253c438c599f9a1bad61eb338baf815d31ec5b2595eaa8ee2ea74
Transactions (2)
Coinbasecfdb0b75a8523d…5b02003d3a8e23
1 in β†’ 1 out7.2400 XPM110 B
APg1nf6g…dJcegxGD
07385a12621116…8e865e9fe01535
3 in β†’ 2 out2.0516 XPM520 B
ARGoBaf4…XoqoCtfSAZVDGE7D…1KdFUjfM
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.

2.053 Γ— 10⁹⁴(95-digit number)
20538118391225075688…14393628863407170800
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
2.053 Γ— 10⁹⁴(95-digit number)
20538118391225075688…14393628863407170801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.107 Γ— 10⁹⁴(95-digit number)
41076236782450151377…28787257726814341601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.215 Γ— 10⁹⁴(95-digit number)
82152473564900302754…57574515453628683201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.643 Γ— 10⁹⁡(96-digit number)
16430494712980060550…15149030907257366401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.286 Γ— 10⁹⁡(96-digit number)
32860989425960121101…30298061814514732801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.572 Γ— 10⁹⁡(96-digit number)
65721978851920242203…60596123629029465601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.314 Γ— 10⁹⁢(97-digit number)
13144395770384048440…21192247258058931201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.628 Γ— 10⁹⁢(97-digit number)
26288791540768096881…42384494516117862401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.257 Γ— 10⁹⁢(97-digit number)
52577583081536193762…84768989032235724801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.051 Γ— 10⁹⁷(98-digit number)
10515516616307238752…69537978064471449601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.103 Γ— 10⁹⁷(98-digit number)
21031033232614477505…39075956128942899201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
4.206 Γ— 10⁹⁷(98-digit number)
42062066465228955010…78151912257885798401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2650864

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 b916f4b34babedaa2781c4e2013665cd70bdcef99e8d871620d49ec199c20fd4

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 #2,650,864 on Chainz β†—
Circulating Supply:57,908,140 XPMΒ·at block #6,832,995 Β· updates every 60s
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