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Home/Chain Registry/Block #2,833,289

Block #2,833,289

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2018, 3:42:19 PM Β· Difficulty 11.7152 Β· 4,005,966 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a29e08823e77905c4de3432b590ee8a7dcbd4d39a00703366a6c8c168cd4d465
View on Chainz β†—

Difficulty

11.715206

Transactions

1

Size

199 B

Version

2

Bits

0bb717c0

Nonce

1,194,654,780

Timestamp

9/10/2018, 3:42:19 PM

Confirmations

4,005,966

Merkle Root

e61d7ab782b8d341fe3d73f91277485bb72714c5aaa5784798154fed26aee4a6
Transactions (1)
Coinbasee61d7ab782b8d3…154fed26aee4a6
1 in β†’ 1 out7.2700 XPM110 B
AZtxQr2F…7grUWrUz
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.

3.665 Γ— 10⁹¹(92-digit number)
36653026477918112860…69214975712610729280
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
3.665 Γ— 10⁹¹(92-digit number)
36653026477918112860…69214975712610729281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.330 Γ— 10⁹¹(92-digit number)
73306052955836225720…38429951425221458561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.466 Γ— 10⁹²(93-digit number)
14661210591167245144…76859902850442917121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.932 Γ— 10⁹²(93-digit number)
29322421182334490288…53719805700885834241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.864 Γ— 10⁹²(93-digit number)
58644842364668980576…07439611401771668481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.172 Γ— 10⁹³(94-digit number)
11728968472933796115…14879222803543336961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.345 Γ— 10⁹³(94-digit number)
23457936945867592230…29758445607086673921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.691 Γ— 10⁹³(94-digit number)
46915873891735184460…59516891214173347841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.383 Γ— 10⁹³(94-digit number)
93831747783470368921…19033782428346695681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.876 Γ— 10⁹⁴(95-digit number)
18766349556694073784…38067564856693391361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.753 Γ— 10⁹⁴(95-digit number)
37532699113388147568…76135129713386782721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
7.506 Γ— 10⁹⁴(95-digit number)
75065398226776295137…52270259426773565441
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 2833289

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 a29e08823e77905c4de3432b590ee8a7dcbd4d39a00703366a6c8c168cd4d465

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 #2,833,289 on Chainz β†—
Circulating Supply:57,958,323 XPMΒ·at block #6,839,254 Β· updates every 60s
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