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Home/Chain Registry/Block #1,046,837

Block #1,046,837

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/6/2015, 1:32:11 AM Β· Difficulty 10.7287 Β· 5,765,435 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
33d614f9d19d67ce47dac681a80c9cfdeb56588f621b36113a5aef8e5eacdc70
View on Chainz β†—

Difficulty

10.728717

Transactions

1

Size

200 B

Version

2

Bits

0aba8d2f

Nonce

1,879,095,459

Timestamp

5/6/2015, 1:32:11 AM

Confirmations

5,765,435

Merkle Root

174b2c79bc61f6d1ff7aa135348e9d5656082e7cbf5f7749a97155a8c49edac1
Transactions (1)
Coinbase174b2c79bc61f6…7155a8c49edac1
1 in β†’ 1 out8.6700 XPM109 B
ARby8jSW…Juct1cKN
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— 10⁹⁷(98-digit number)
12939083107890972610…32167357207586017280
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— 10⁹⁷(98-digit number)
12939083107890972610…32167357207586017281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.587 Γ— 10⁹⁷(98-digit number)
25878166215781945220…64334714415172034561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.175 Γ— 10⁹⁷(98-digit number)
51756332431563890440…28669428830344069121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.035 Γ— 10⁹⁸(99-digit number)
10351266486312778088…57338857660688138241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.070 Γ— 10⁹⁸(99-digit number)
20702532972625556176…14677715321376276481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.140 Γ— 10⁹⁸(99-digit number)
41405065945251112352…29355430642752552961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.281 Γ— 10⁹⁸(99-digit number)
82810131890502224705…58710861285505105921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.656 Γ— 10⁹⁹(100-digit number)
16562026378100444941…17421722571010211841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.312 Γ— 10⁹⁹(100-digit number)
33124052756200889882…34843445142020423681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.624 Γ— 10⁹⁹(100-digit number)
66248105512401779764…69686890284040847361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1046837

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 33d614f9d19d67ce47dac681a80c9cfdeb56588f621b36113a5aef8e5eacdc70

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 #1,046,837 on Chainz β†—
Circulating Supply:57,742,193 XPMΒ·at block #6,812,271 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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