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Home/Chain Registry/Block #1,678,347

Block #1,678,347

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/18/2016, 11:14:52 AM Β· Difficulty 10.6937 Β· 5,167,306 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1af77d31c56f4f9a64243bcf12329457c6088dc42be7c0302419410dc445c54e
View on Chainz β†—

Difficulty

10.693714

Transactions

1

Size

200 B

Version

2

Bits

0ab19745

Nonce

1,641,016,500

Timestamp

7/18/2016, 11:14:52 AM

Confirmations

5,167,306

Merkle Root

514fabea9664a221fb9ac0e56c5777c8c983f634924c5929ca68b74d432cf1f8
Transactions (1)
Coinbase514fabea9664a2…68b74d432cf1f8
1 in β†’ 1 out8.7300 XPM110 B
AP4YFtSP…cDicVrxT
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.

8.071 Γ— 10⁹³(94-digit number)
80717064426027491833…93648042587659186660
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
8.071 Γ— 10⁹³(94-digit number)
80717064426027491833…93648042587659186659
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.614 Γ— 10⁹⁴(95-digit number)
16143412885205498366…87296085175318373319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.228 Γ— 10⁹⁴(95-digit number)
32286825770410996733…74592170350636746639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.457 Γ— 10⁹⁴(95-digit number)
64573651540821993466…49184340701273493279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.291 Γ— 10⁹⁡(96-digit number)
12914730308164398693…98368681402546986559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.582 Γ— 10⁹⁡(96-digit number)
25829460616328797386…96737362805093973119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.165 Γ— 10⁹⁡(96-digit number)
51658921232657594773…93474725610187946239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.033 Γ— 10⁹⁢(97-digit number)
10331784246531518954…86949451220375892479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.066 Γ— 10⁹⁢(97-digit number)
20663568493063037909…73898902440751784959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.132 Γ— 10⁹⁢(97-digit number)
41327136986126075818…47797804881503569919
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 1678347

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 1af77d31c56f4f9a64243bcf12329457c6088dc42be7c0302419410dc445c54e

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 #1,678,347 on Chainz β†—
Circulating Supply:58,009,672 XPMΒ·at block #6,845,652 Β· updates every 60s
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