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Block #2,634,930

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 1:53:28 AM Β· Difficulty 11.2800 Β· 4,203,349 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c7539916e0b06609169f2a6a0e4cbee7380e05abd4b9744007e34f637e6fbd9c
View on Chainz β†—

Difficulty

11.279969

Transactions

1

Size

201 B

Version

2

Bits

0b47ac13

Nonce

245,343,846

Timestamp

4/29/2018, 1:53:28 AM

Confirmations

4,203,349

Merkle Root

5b86214df233f301c16832b302552b11bc75407c890278da3ad23f451af93dcf
Transactions (1)
Coinbase5b86214df233f3…d23f451af93dcf
1 in β†’ 1 out7.8500 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.965 Γ— 10⁹⁢(97-digit number)
19659595454866466172…19045966142068527360
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
1.965 Γ— 10⁹⁢(97-digit number)
19659595454866466172…19045966142068527361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.931 Γ— 10⁹⁢(97-digit number)
39319190909732932344…38091932284137054721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.863 Γ— 10⁹⁢(97-digit number)
78638381819465864688…76183864568274109441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.572 Γ— 10⁹⁷(98-digit number)
15727676363893172937…52367729136548218881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.145 Γ— 10⁹⁷(98-digit number)
31455352727786345875…04735458273096437761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.291 Γ— 10⁹⁷(98-digit number)
62910705455572691750…09470916546192875521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.258 Γ— 10⁹⁸(99-digit number)
12582141091114538350…18941833092385751041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.516 Γ— 10⁹⁸(99-digit number)
25164282182229076700…37883666184771502081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.032 Γ— 10⁹⁸(99-digit number)
50328564364458153400…75767332369543004161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.006 Γ— 10⁹⁹(100-digit number)
10065712872891630680…51534664739086008321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.013 Γ— 10⁹⁹(100-digit number)
20131425745783261360…03069329478172016641
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 2634930

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 c7539916e0b06609169f2a6a0e4cbee7380e05abd4b9744007e34f637e6fbd9c

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 #2,634,930 on Chainz β†—
Circulating Supply:57,950,513 XPMΒ·at block #6,838,278 Β· updates every 60s
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