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Home/Chain Registry/Block #1,403,792

Block #1,403,792

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/8/2016, 1:42:12 AM Β· Difficulty 10.8063 Β· 5,438,977 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6c897cabc8eebcf97b44330c433b322c5f335d08b5084b6bf64acb50dac51396
View on Chainz β†—

Difficulty

10.806327

Transactions

1

Size

201 B

Version

2

Bits

0ace6b76

Nonce

698,667,132

Timestamp

1/8/2016, 1:42:12 AM

Confirmations

5,438,977

Merkle Root

05ebd9a074a4c0a4e18a43ab2e2510d62563f53fbf0da687a1df6bca1e494727
Transactions (1)
Coinbase05ebd9a074a4c0…df6bca1e494727
1 in β†’ 1 out8.5500 XPM110 B
ASPRm59r…SRsQJWxS
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.

2.091 Γ— 10⁹⁢(97-digit number)
20914852758863594850…14535484714723481600
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
2.091 Γ— 10⁹⁢(97-digit number)
20914852758863594850…14535484714723481601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.182 Γ— 10⁹⁢(97-digit number)
41829705517727189701…29070969429446963201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.365 Γ— 10⁹⁢(97-digit number)
83659411035454379402…58141938858893926401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.673 Γ— 10⁹⁷(98-digit number)
16731882207090875880…16283877717787852801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.346 Γ— 10⁹⁷(98-digit number)
33463764414181751760…32567755435575705601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.692 Γ— 10⁹⁷(98-digit number)
66927528828363503521…65135510871151411201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.338 Γ— 10⁹⁸(99-digit number)
13385505765672700704…30271021742302822401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.677 Γ— 10⁹⁸(99-digit number)
26771011531345401408…60542043484605644801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.354 Γ— 10⁹⁸(99-digit number)
53542023062690802817…21084086969211289601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.070 Γ— 10⁹⁹(100-digit number)
10708404612538160563…42168173938422579201
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 1403792

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 6c897cabc8eebcf97b44330c433b322c5f335d08b5084b6bf64acb50dac51396

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 #1,403,792 on Chainz β†—
Circulating Supply:57,986,491 XPMΒ·at block #6,842,768 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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