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Block #2,696,437

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/8/2018, 2:42:04 AM Β· Difficulty 11.6674 Β· 4,146,457 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
abaaf0d3d2cdc34c0589d06ff0256a265e8b6d9492766b8163600e8c6626e1d0
View on Chainz β†—

Difficulty

11.667441

Transactions

1

Size

201 B

Version

2

Bits

0baadd6d

Nonce

58,482,771

Timestamp

6/8/2018, 2:42:04 AM

Confirmations

4,146,457

Merkle Root

db31a90532598be27c9cfc2246481a6372b3501e497aecb8eb0a62a40d2afa89
Transactions (1)
Coinbasedb31a90532598b…0a62a40d2afa89
1 in β†’ 1 out7.3300 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.

1.636 Γ— 10⁹⁢(97-digit number)
16367845738333554584…15184946618956318720
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
1.636 Γ— 10⁹⁢(97-digit number)
16367845738333554584…15184946618956318721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.273 Γ— 10⁹⁢(97-digit number)
32735691476667109169…30369893237912637441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.547 Γ— 10⁹⁢(97-digit number)
65471382953334218338…60739786475825274881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.309 Γ— 10⁹⁷(98-digit number)
13094276590666843667…21479572951650549761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.618 Γ— 10⁹⁷(98-digit number)
26188553181333687335…42959145903301099521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.237 Γ— 10⁹⁷(98-digit number)
52377106362667374670…85918291806602199041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.047 Γ— 10⁹⁸(99-digit number)
10475421272533474934…71836583613204398081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.095 Γ— 10⁹⁸(99-digit number)
20950842545066949868…43673167226408796161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.190 Γ— 10⁹⁸(99-digit number)
41901685090133899736…87346334452817592321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.380 Γ— 10⁹⁸(99-digit number)
83803370180267799473…74692668905635184641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.676 Γ— 10⁹⁹(100-digit number)
16760674036053559894…49385337811270369281
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 2696437

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 abaaf0d3d2cdc34c0589d06ff0256a265e8b6d9492766b8163600e8c6626e1d0

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 #2,696,437 on Chainz β†—
Circulating Supply:57,987,499 XPMΒ·at block #6,842,893 Β· updates every 60s
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