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Home/Chain Registry/Block #2,641,165

Block #2,641,165

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 6:25:28 AM Β· Difficulty 11.6096 Β· 4,201,624 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7816dcf89aae225d4d2b667dd4133a4b1863f0d34a4fcf00783f87fc0d9b45a8
View on Chainz β†—

Difficulty

11.609603

Transactions

1

Size

199 B

Version

2

Bits

0b9c0ef0

Nonce

221,957,447

Timestamp

5/1/2018, 6:25:28 AM

Confirmations

4,201,624

Merkle Root

bc8175d279b95a68195608f4d41324de65367c520cf05c948b97bab6eb470ae9
Transactions (1)
Coinbasebc8175d279b95a…97bab6eb470ae9
1 in β†’ 1 out7.4100 XPM110 B
AU1FV2rW…p6en5ViR
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.

3.230 Γ— 10⁹¹(92-digit number)
32300553785185268806…65093090801157291520
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
3.230 Γ— 10⁹¹(92-digit number)
32300553785185268806…65093090801157291521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.460 Γ— 10⁹¹(92-digit number)
64601107570370537613…30186181602314583041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.292 Γ— 10⁹²(93-digit number)
12920221514074107522…60372363204629166081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.584 Γ— 10⁹²(93-digit number)
25840443028148215045…20744726409258332161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.168 Γ— 10⁹²(93-digit number)
51680886056296430090…41489452818516664321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.033 Γ— 10⁹³(94-digit number)
10336177211259286018…82978905637033328641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.067 Γ— 10⁹³(94-digit number)
20672354422518572036…65957811274066657281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.134 Γ— 10⁹³(94-digit number)
41344708845037144072…31915622548133314561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.268 Γ— 10⁹³(94-digit number)
82689417690074288144…63831245096266629121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.653 Γ— 10⁹⁴(95-digit number)
16537883538014857628…27662490192533258241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.307 Γ— 10⁹⁴(95-digit number)
33075767076029715257…55324980385066516481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
6.615 Γ— 10⁹⁴(95-digit number)
66151534152059430515…10649960770133032961
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2641165

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 7816dcf89aae225d4d2b667dd4133a4b1863f0d34a4fcf00783f87fc0d9b45a8

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 #2,641,165 on Chainz β†—
Circulating Supply:57,986,650 XPMΒ·at block #6,842,788 Β· updates every 60s
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