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Block #846,635

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/9/2014, 6:14:40 PM Β· Difficulty 10.9722 Β· 5,986,720 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b2c696ffa84766d70bdae3a77f532a2307f9c9675421ab6d2d402ffca61de49d
View on Chainz β†—

Height

#846,635

Difficulty

10.972217

Transactions

1

Size

207 B

Version

2

Bits

0af8e33e

Nonce

334,382,503

Timestamp

12/9/2014, 6:14:40 PM

Confirmations

5,986,720

Merkle Root

dedf3c7d16c20d39b36ec33aca4875eebe376a51f6aa4de60c20f6ff5dd399a0
Transactions (1)
Coinbasededf3c7d16c20d…20f6ff5dd399a0
1 in β†’ 1 out8.2900 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.356 Γ— 10⁹⁸(99-digit number)
13566157599107398697…91287160444182174720
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
1.356 Γ— 10⁹⁸(99-digit number)
13566157599107398697…91287160444182174719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.713 Γ— 10⁹⁸(99-digit number)
27132315198214797395…82574320888364349439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.426 Γ— 10⁹⁸(99-digit number)
54264630396429594791…65148641776728698879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.085 Γ— 10⁹⁹(100-digit number)
10852926079285918958…30297283553457397759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.170 Γ— 10⁹⁹(100-digit number)
21705852158571837916…60594567106914795519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.341 Γ— 10⁹⁹(100-digit number)
43411704317143675832…21189134213829591039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.682 Γ— 10⁹⁹(100-digit number)
86823408634287351665…42378268427659182079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.736 Γ— 10¹⁰⁰(101-digit number)
17364681726857470333…84756536855318364159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.472 Γ— 10¹⁰⁰(101-digit number)
34729363453714940666…69513073710636728319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.945 Γ— 10¹⁰⁰(101-digit number)
69458726907429881332…39026147421273456639
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 846635

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 b2c696ffa84766d70bdae3a77f532a2307f9c9675421ab6d2d402ffca61de49d

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 #846,635 on Chainz β†—
Circulating Supply:57,911,038 XPMΒ·at block #6,833,354 Β· updates every 60s
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