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Home/Chain Registry/Block #3,174,002

Block #3,174,002

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/8/2019, 9:48:25 PM Β· Difficulty 11.3053 Β· 3,668,500 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0d2f08977a54a904b575b99f351b4e9fd9f8fad2a325aaf41093ef1ccb511a30
View on Chainz β†—

Difficulty

11.305292

Transactions

1

Size

200 B

Version

2

Bits

0b4e27a5

Nonce

1,051,994,149

Timestamp

5/8/2019, 9:48:25 PM

Confirmations

3,668,500

Merkle Root

01f68a8cc3a944a28928215cf592ed932b00943885bc40a66de9d33c17cfbe70
Transactions (1)
Coinbase01f68a8cc3a944…e9d33c17cfbe70
1 in β†’ 1 out7.8100 XPM110 B
ARbm48qR…9xQc8DBX
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.

7.603 Γ— 10⁹⁴(95-digit number)
76033165383180233584…93449607245014260750
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
7.603 Γ— 10⁹⁴(95-digit number)
76033165383180233584…93449607245014260751
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.520 Γ— 10⁹⁡(96-digit number)
15206633076636046716…86899214490028521501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.041 Γ— 10⁹⁡(96-digit number)
30413266153272093433…73798428980057043001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.082 Γ— 10⁹⁡(96-digit number)
60826532306544186867…47596857960114086001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.216 Γ— 10⁹⁢(97-digit number)
12165306461308837373…95193715920228172001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.433 Γ— 10⁹⁢(97-digit number)
24330612922617674747…90387431840456344001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.866 Γ— 10⁹⁢(97-digit number)
48661225845235349494…80774863680912688001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.732 Γ— 10⁹⁢(97-digit number)
97322451690470698988…61549727361825376001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.946 Γ— 10⁹⁷(98-digit number)
19464490338094139797…23099454723650752001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.892 Γ— 10⁹⁷(98-digit number)
38928980676188279595…46198909447301504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.785 Γ— 10⁹⁷(98-digit number)
77857961352376559190…92397818894603008001
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 3174002

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 0d2f08977a54a904b575b99f351b4e9fd9f8fad2a325aaf41093ef1ccb511a30

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 #3,174,002 on Chainz β†—
Circulating Supply:57,984,433 XPMΒ·at block #6,842,501 Β· updates every 60s
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