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Home/Chain Registry/Block #1,403,794

Block #1,403,794

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/8/2016, 1:43:30 AM Β· Difficulty 10.8064 Β· 5,439,259 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2e70d1d4593d7ac182b1fa648f89748c0aad5da072f08eba1443e78acf2c4c6e
View on Chainz β†—

Difficulty

10.806370

Transactions

1

Size

199 B

Version

2

Bits

0ace6e3c

Nonce

306,511,894

Timestamp

1/8/2016, 1:43:30 AM

Confirmations

5,439,259

Merkle Root

cfd6f8bfe9f1c8d291fa8ca9dd48be7fdce9bd0b64e2f69918148faaef81a6ba
Transactions (1)
Coinbasecfd6f8bfe9f1c8…148faaef81a6ba
1 in β†’ 1 out8.5500 XPM109 B
AZz4Eg4G…4byK8czD
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.

2.050 Γ— 10⁹⁡(96-digit number)
20502177154629407837…89037135882443851200
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
2.050 Γ— 10⁹⁡(96-digit number)
20502177154629407837…89037135882443851201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.100 Γ— 10⁹⁡(96-digit number)
41004354309258815674…78074271764887702401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.200 Γ— 10⁹⁡(96-digit number)
82008708618517631348…56148543529775404801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.640 Γ— 10⁹⁢(97-digit number)
16401741723703526269…12297087059550809601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.280 Γ— 10⁹⁢(97-digit number)
32803483447407052539…24594174119101619201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.560 Γ— 10⁹⁢(97-digit number)
65606966894814105078…49188348238203238401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.312 Γ— 10⁹⁷(98-digit number)
13121393378962821015…98376696476406476801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.624 Γ— 10⁹⁷(98-digit number)
26242786757925642031…96753392952812953601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.248 Γ— 10⁹⁷(98-digit number)
52485573515851284062…93506785905625907201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.049 Γ— 10⁹⁸(99-digit number)
10497114703170256812…87013571811251814401
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 1403794

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 2e70d1d4593d7ac182b1fa648f89748c0aad5da072f08eba1443e78acf2c4c6e

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 #1,403,794 on Chainz β†—
Circulating Supply:57,988,782 XPMΒ·at block #6,843,052 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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