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Home/Chain Registry/Block #2,235,235

Block #2,235,235

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/3/2017, 2:24:19 PM Β· Difficulty 10.9456 Β· 4,609,732 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
234a15fd436ec80aba2bff727b6067f06bb5eba6e2b9a401ac6532ba9c27a1ff
View on Chainz β†—

Difficulty

10.945625

Transactions

2

Size

1.25 KB

Version

2

Bits

0af21477

Nonce

1,198,105,358

Timestamp

8/3/2017, 2:24:19 PM

Confirmations

4,609,732

Merkle Root

4e136d16b9dc9571c9bd32d1a95176f64b5a085c22736538712eb404ca4266b7
Transactions (2)
Coinbasea6e3a7c886a5d5…f9e358cbe4ea0b
1 in β†’ 1 out8.3500 XPM110 B
ASTFHKwh…dkmBxnoc
61b5cf1abe3b04…4d14c193d32491
7 in β†’ 1 out729.9900 XPM1.06 KB
AdGeXqyk…7w6YKmWt
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.

3.677 Γ— 10⁹²(93-digit number)
36776911006004208495…61764159541993514840
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
3.677 Γ— 10⁹²(93-digit number)
36776911006004208495…61764159541993514839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.355 Γ— 10⁹²(93-digit number)
73553822012008416990…23528319083987029679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.471 Γ— 10⁹³(94-digit number)
14710764402401683398…47056638167974059359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.942 Γ— 10⁹³(94-digit number)
29421528804803366796…94113276335948118719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.884 Γ— 10⁹³(94-digit number)
58843057609606733592…88226552671896237439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.176 Γ— 10⁹⁴(95-digit number)
11768611521921346718…76453105343792474879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.353 Γ— 10⁹⁴(95-digit number)
23537223043842693437…52906210687584949759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.707 Γ— 10⁹⁴(95-digit number)
47074446087685386874…05812421375169899519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.414 Γ— 10⁹⁴(95-digit number)
94148892175370773748…11624842750339799039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.882 Γ— 10⁹⁡(96-digit number)
18829778435074154749…23249685500679598079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.765 Γ— 10⁹⁡(96-digit number)
37659556870148309499…46499371001359196159
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 2235235

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 234a15fd436ec80aba2bff727b6067f06bb5eba6e2b9a401ac6532ba9c27a1ff

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 #2,235,235 on Chainz β†—
Circulating Supply:58,004,153 XPMΒ·at block #6,844,966 Β· updates every 60s
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