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Block #2,622,644

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/20/2018, 7:04:55 PM Β· Difficulty 11.2269 Β· 4,219,599 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f6ab57f26ac9c3cd328ea9ee156d38c6c15193e6f717d7e0927a442c3dfa93a4
View on Chainz β†—

Difficulty

11.226947

Transactions

1

Size

200 B

Version

2

Bits

0b3a1931

Nonce

1,081,515,243

Timestamp

4/20/2018, 7:04:55 PM

Confirmations

4,219,599

Merkle Root

ece90531cb047de8c258c89c7a55bcd270c0179240522bd0b8a5f4e91dcbf62d
Transactions (1)
Coinbaseece90531cb047d…a5f4e91dcbf62d
1 in β†’ 1 out7.9200 XPM109 B
AZEwm8Yq…C6L57ixf
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.

2.469 Γ— 10⁹⁢(97-digit number)
24697588095390499052…07442013052630922240
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
2.469 Γ— 10⁹⁢(97-digit number)
24697588095390499052…07442013052630922241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.939 Γ— 10⁹⁢(97-digit number)
49395176190780998105…14884026105261844481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.879 Γ— 10⁹⁢(97-digit number)
98790352381561996210…29768052210523688961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.975 Γ— 10⁹⁷(98-digit number)
19758070476312399242…59536104421047377921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.951 Γ— 10⁹⁷(98-digit number)
39516140952624798484…19072208842094755841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.903 Γ— 10⁹⁷(98-digit number)
79032281905249596968…38144417684189511681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.580 Γ— 10⁹⁸(99-digit number)
15806456381049919393…76288835368379023361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.161 Γ— 10⁹⁸(99-digit number)
31612912762099838787…52577670736758046721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.322 Γ— 10⁹⁸(99-digit number)
63225825524199677574…05155341473516093441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.264 Γ— 10⁹⁹(100-digit number)
12645165104839935514…10310682947032186881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.529 Γ— 10⁹⁹(100-digit number)
25290330209679871029…20621365894064373761
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 2622644

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 f6ab57f26ac9c3cd328ea9ee156d38c6c15193e6f717d7e0927a442c3dfa93a4

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 #2,622,644 on Chainz β†—
Circulating Supply:57,982,342 XPMΒ·at block #6,842,242 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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