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Home/Chain Registry/Block #2,636,306

Block #2,636,306

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/29/2018, 1:05:03 PM Β· Difficulty 11.3740 Β· 4,194,323 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2c31f72a780c81fc1594ef00d0dfa7cd1625e13153567f7cd6f8e248b26372c6
View on Chainz β†—

Difficulty

11.373955

Transactions

1

Size

201 B

Version

2

Bits

0b5fbb7c

Nonce

96,138,955

Timestamp

4/29/2018, 1:05:03 PM

Confirmations

4,194,323

Merkle Root

c628019d241dc42c89cd67aa9d5d3bd7786d5cf6720ef0c7e4a3bfeb931847bd
Transactions (1)
Coinbasec628019d241dc4…a3bfeb931847bd
1 in β†’ 1 out7.7200 XPM110 B
ALuBGq62…TxRbpVp7
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.

2.819 Γ— 10⁹⁢(97-digit number)
28197414174670761711…70602611727146188800
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.819 Γ— 10⁹⁢(97-digit number)
28197414174670761711…70602611727146188799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.639 Γ— 10⁹⁢(97-digit number)
56394828349341523422…41205223454292377599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.127 Γ— 10⁹⁷(98-digit number)
11278965669868304684…82410446908584755199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.255 Γ— 10⁹⁷(98-digit number)
22557931339736609368…64820893817169510399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.511 Γ— 10⁹⁷(98-digit number)
45115862679473218737…29641787634339020799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.023 Γ— 10⁹⁷(98-digit number)
90231725358946437475…59283575268678041599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.804 Γ— 10⁹⁸(99-digit number)
18046345071789287495…18567150537356083199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.609 Γ— 10⁹⁸(99-digit number)
36092690143578574990…37134301074712166399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.218 Γ— 10⁹⁸(99-digit number)
72185380287157149980…74268602149424332799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.443 Γ— 10⁹⁹(100-digit number)
14437076057431429996…48537204298848665599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.887 Γ— 10⁹⁹(100-digit number)
28874152114862859992…97074408597697331199
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2636306

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 2c31f72a780c81fc1594ef00d0dfa7cd1625e13153567f7cd6f8e248b26372c6

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 #2,636,306 on Chainz β†—
Circulating Supply:57,889,154 XPMΒ·at block #6,830,628 Β· updates every 60s
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