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Block #2,633,483

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 11:20:28 AM Β· Difficulty 11.1931 Β· 4,203,199 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f0bc8c1eca0279dde2a1716257d90f8bd0018ce95690aedc3bed580f913050c4
View on Chainz β†—

Difficulty

11.193128

Transactions

1

Size

201 B

Version

2

Bits

0b3170d6

Nonce

587,667,986

Timestamp

4/28/2018, 11:20:28 AM

Confirmations

4,203,199

Merkle Root

6e30770d2643c19afa85eaff26e52d85a9604a17b6860e0aee8d9594952ef7d6
Transactions (1)
Coinbase6e30770d2643c1…8d9594952ef7d6
1 in β†’ 1 out7.9700 XPM110 B
AQmhGuGs…gQyzDuvz
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.

1.634 Γ— 10⁹⁸(99-digit number)
16346313482269460758…31779577765200199680
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
1.634 Γ— 10⁹⁸(99-digit number)
16346313482269460758…31779577765200199681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.269 Γ— 10⁹⁸(99-digit number)
32692626964538921517…63559155530400399361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.538 Γ— 10⁹⁸(99-digit number)
65385253929077843034…27118311060800798721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.307 Γ— 10⁹⁹(100-digit number)
13077050785815568606…54236622121601597441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.615 Γ— 10⁹⁹(100-digit number)
26154101571631137213…08473244243203194881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.230 Γ— 10⁹⁹(100-digit number)
52308203143262274427…16946488486406389761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.046 Γ— 10¹⁰⁰(101-digit number)
10461640628652454885…33892976972812779521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.092 Γ— 10¹⁰⁰(101-digit number)
20923281257304909771…67785953945625559041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.184 Γ— 10¹⁰⁰(101-digit number)
41846562514609819542…35571907891251118081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.369 Γ— 10¹⁰⁰(101-digit number)
83693125029219639084…71143815782502236161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.673 Γ— 10¹⁰¹(102-digit number)
16738625005843927816…42287631565004472321
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 2633483

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 f0bc8c1eca0279dde2a1716257d90f8bd0018ce95690aedc3bed580f913050c4

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 #2,633,483 on Chainz β†—
Circulating Supply:57,937,736 XPMΒ·at block #6,836,681 Β· updates every 60s
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