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Home/Chain Registry/Block #2,655,361

Block #2,655,361

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/10/2018, 3:12:39 AM Β· Difficulty 11.7066 Β· 4,178,451 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dd0eba9764a767ab9b69317ebab0438c486072f9dcdfa55bc1d717575a006e3c
View on Chainz β†—

Difficulty

11.706596

Transactions

2

Size

425 B

Version

2

Bits

0bb4e372

Nonce

965,526,550

Timestamp

5/10/2018, 3:12:39 AM

Confirmations

4,178,451

Merkle Root

a1288e300bf059cb1296d004e6387f992866415cbcd05d3325c0addddb4aff32
Transactions (2)
Coinbasecd5bfdf6dca4e7…29025c83c0a4dd
1 in β†’ 1 out7.2900 XPM110 B
ANXHTNdc…S1h3hyp9
f20fbbc5f3a146…bebf48629a5039
1 in β†’ 2 out153.2897 XPM225 B
AHGujYHK…tXPWLPBUAJJgmq8q…7itrxzz5
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.

4.852 Γ— 10⁹⁴(95-digit number)
48525281025831968606…03583898941290617600
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
4.852 Γ— 10⁹⁴(95-digit number)
48525281025831968606…03583898941290617601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.705 Γ— 10⁹⁴(95-digit number)
97050562051663937213…07167797882581235201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.941 Γ— 10⁹⁡(96-digit number)
19410112410332787442…14335595765162470401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.882 Γ— 10⁹⁡(96-digit number)
38820224820665574885…28671191530324940801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.764 Γ— 10⁹⁡(96-digit number)
77640449641331149770…57342383060649881601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.552 Γ— 10⁹⁢(97-digit number)
15528089928266229954…14684766121299763201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.105 Γ— 10⁹⁢(97-digit number)
31056179856532459908…29369532242599526401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.211 Γ— 10⁹⁢(97-digit number)
62112359713064919816…58739064485199052801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.242 Γ— 10⁹⁷(98-digit number)
12422471942612983963…17478128970398105601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.484 Γ— 10⁹⁷(98-digit number)
24844943885225967926…34956257940796211201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.968 Γ— 10⁹⁷(98-digit number)
49689887770451935853…69912515881592422401
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 2655361

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 dd0eba9764a767ab9b69317ebab0438c486072f9dcdfa55bc1d717575a006e3c

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 #2,655,361 on Chainz β†—
Circulating Supply:57,914,720 XPMΒ·at block #6,833,811 Β· updates every 60s
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