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Home/Chain Registry/Block #2,835,539

Block #2,835,539

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/12/2018, 5:11:21 AM Β· Difficulty 11.7153 Β· 4,006,406 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
67cd912b7116c7ae2e9a99b7958354cae36f9df80f3ecc93484c7f9b90ab363f
View on Chainz β†—

Difficulty

11.715334

Transactions

1

Size

201 B

Version

2

Bits

0bb72026

Nonce

1,859,954,172

Timestamp

9/12/2018, 5:11:21 AM

Confirmations

4,006,406

Merkle Root

813a271184b8d46bf5318a463196fd092f41ac055ada8fd48ece24a15f35ebe1
Transactions (1)
Coinbase813a271184b8d4…ce24a15f35ebe1
1 in β†’ 1 out7.2700 XPM110 B
AZtxQr2F…7grUWrUz
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.

5.559 Γ— 10⁹⁢(97-digit number)
55599404412922342725…30460588442756311040
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
5.559 Γ— 10⁹⁢(97-digit number)
55599404412922342725…30460588442756311041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.111 Γ— 10⁹⁷(98-digit number)
11119880882584468545…60921176885512622081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.223 Γ— 10⁹⁷(98-digit number)
22239761765168937090…21842353771025244161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.447 Γ— 10⁹⁷(98-digit number)
44479523530337874180…43684707542050488321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.895 Γ— 10⁹⁷(98-digit number)
88959047060675748361…87369415084100976641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.779 Γ— 10⁹⁸(99-digit number)
17791809412135149672…74738830168201953281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.558 Γ— 10⁹⁸(99-digit number)
35583618824270299344…49477660336403906561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.116 Γ— 10⁹⁸(99-digit number)
71167237648540598689…98955320672807813121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.423 Γ— 10⁹⁹(100-digit number)
14233447529708119737…97910641345615626241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.846 Γ— 10⁹⁹(100-digit number)
28466895059416239475…95821282691231252481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.693 Γ— 10⁹⁹(100-digit number)
56933790118832478951…91642565382462504961
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 2835539

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 67cd912b7116c7ae2e9a99b7958354cae36f9df80f3ecc93484c7f9b90ab363f

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 #2,835,539 on Chainz β†—
Circulating Supply:57,979,941 XPMΒ·at block #6,841,944 Β· updates every 60s
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