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Home/Chain Registry/Block #2,642,770

Block #2,642,770

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 8:46:05 PM Β· Difficulty 11.6632 Β· 4,188,533 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
21334de1c7b72cfa5082af02e34221273e29cdb468769df31d303299c09c1a28
View on Chainz β†—

Difficulty

11.663243

Transactions

1

Size

201 B

Version

2

Bits

0ba9ca4a

Nonce

10,727,219

Timestamp

5/1/2018, 8:46:05 PM

Confirmations

4,188,533

Merkle Root

c9612f99f1380673bb311f09fffd1c6c867b519adae4129b3a5ef6d798963494
Transactions (1)
Coinbasec9612f99f13806…5ef6d798963494
1 in β†’ 1 out7.3400 XPM110 B
AVHTTCFJ…tQ2kopGh
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.

1.293 Γ— 10⁹⁢(97-digit number)
12939736985616619420…19902659568338658880
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
1.293 Γ— 10⁹⁢(97-digit number)
12939736985616619420…19902659568338658881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.587 Γ— 10⁹⁢(97-digit number)
25879473971233238841…39805319136677317761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.175 Γ— 10⁹⁢(97-digit number)
51758947942466477683…79610638273354635521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.035 Γ— 10⁹⁷(98-digit number)
10351789588493295536…59221276546709271041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.070 Γ— 10⁹⁷(98-digit number)
20703579176986591073…18442553093418542081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.140 Γ— 10⁹⁷(98-digit number)
41407158353973182146…36885106186837084161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.281 Γ— 10⁹⁷(98-digit number)
82814316707946364293…73770212373674168321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.656 Γ— 10⁹⁸(99-digit number)
16562863341589272858…47540424747348336641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.312 Γ— 10⁹⁸(99-digit number)
33125726683178545717…95080849494696673281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.625 Γ— 10⁹⁸(99-digit number)
66251453366357091434…90161698989393346561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.325 Γ— 10⁹⁹(100-digit number)
13250290673271418286…80323397978786693121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
2.650 Γ— 10⁹⁹(100-digit number)
26500581346542836573…60646795957573386241
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 2642770

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 21334de1c7b72cfa5082af02e34221273e29cdb468769df31d303299c09c1a28

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 #2,642,770 on Chainz β†—
Circulating Supply:57,894,572 XPMΒ·at block #6,831,302 Β· updates every 60s
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