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Home/Chain Registry/Block #2,644,117

Block #2,644,117

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 8:51:55 AM Β· Difficulty 11.7023 Β· 4,201,532 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7d88171a7fe5288a24ccb15d5ca43d344c7bf641b063d4a1c16216b7a29e7695
View on Chainz β†—

Difficulty

11.702336

Transactions

1

Size

200 B

Version

2

Bits

0bb3cc47

Nonce

223,506,594

Timestamp

5/2/2018, 8:51:55 AM

Confirmations

4,201,532

Merkle Root

808b30fff971586ae2c90763659d6f457383ea1199e674d51cd1660681f25483
Transactions (1)
Coinbase808b30fff97158…d1660681f25483
1 in β†’ 1 out7.2900 XPM110 B
AG8rGxgX…wQe5Dg5o
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.

7.300 Γ— 10⁹⁴(95-digit number)
73004454088872367575…72484821994977954560
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
7.300 Γ— 10⁹⁴(95-digit number)
73004454088872367575…72484821994977954561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.460 Γ— 10⁹⁡(96-digit number)
14600890817774473515…44969643989955909121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.920 Γ— 10⁹⁡(96-digit number)
29201781635548947030…89939287979911818241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.840 Γ— 10⁹⁡(96-digit number)
58403563271097894060…79878575959823636481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.168 Γ— 10⁹⁢(97-digit number)
11680712654219578812…59757151919647272961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.336 Γ— 10⁹⁢(97-digit number)
23361425308439157624…19514303839294545921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.672 Γ— 10⁹⁢(97-digit number)
46722850616878315248…39028607678589091841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.344 Γ— 10⁹⁢(97-digit number)
93445701233756630497…78057215357178183681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.868 Γ— 10⁹⁷(98-digit number)
18689140246751326099…56114430714356367361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.737 Γ— 10⁹⁷(98-digit number)
37378280493502652198…12228861428712734721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.475 Γ— 10⁹⁷(98-digit number)
74756560987005304397…24457722857425469441
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 2644117

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 7d88171a7fe5288a24ccb15d5ca43d344c7bf641b063d4a1c16216b7a29e7695

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 #2,644,117 on Chainz β†—
Circulating Supply:58,009,641 XPMΒ·at block #6,845,648 Β· updates every 60s
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