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Home/Chain Registry/Block #2,644,788

Block #2,644,788

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 3:37:36 PM Β· Difficulty 11.7176 Β· 4,186,305 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5e4ab27cd0c5ee7c7ef674af7354339b9beae31c34efae22232c28f47166e89a
View on Chainz β†—

Difficulty

11.717632

Transactions

1

Size

201 B

Version

2

Bits

0bb7b6bc

Nonce

1,072,139,370

Timestamp

5/2/2018, 3:37:36 PM

Confirmations

4,186,305

Merkle Root

e46efd0df4ab8aa63ede6c2da0e2bd5f0e09a13eb87f6409ced31ac437d6ec26
Transactions (1)
Coinbasee46efd0df4ab8a…d31ac437d6ec26
1 in β†’ 1 out7.2700 XPM110 B
AStHEkq7…iJ3WScnt
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.

6.107 Γ— 10⁹⁢(97-digit number)
61077596777959067036…90840916200670902400
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
6.107 Γ— 10⁹⁢(97-digit number)
61077596777959067036…90840916200670902401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.221 Γ— 10⁹⁷(98-digit number)
12215519355591813407…81681832401341804801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.443 Γ— 10⁹⁷(98-digit number)
24431038711183626814…63363664802683609601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.886 Γ— 10⁹⁷(98-digit number)
48862077422367253629…26727329605367219201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.772 Γ— 10⁹⁷(98-digit number)
97724154844734507259…53454659210734438401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.954 Γ— 10⁹⁸(99-digit number)
19544830968946901451…06909318421468876801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.908 Γ— 10⁹⁸(99-digit number)
39089661937893802903…13818636842937753601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.817 Γ— 10⁹⁸(99-digit number)
78179323875787605807…27637273685875507201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.563 Γ— 10⁹⁹(100-digit number)
15635864775157521161…55274547371751014401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.127 Γ— 10⁹⁹(100-digit number)
31271729550315042322…10549094743502028801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.254 Γ— 10⁹⁹(100-digit number)
62543459100630084645…21098189487004057601
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 2644788

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 5e4ab27cd0c5ee7c7ef674af7354339b9beae31c34efae22232c28f47166e89a

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 #2,644,788 on Chainz β†—
Circulating Supply:57,892,886 XPMΒ·at block #6,831,092 Β· updates every 60s
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