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Block #850,728

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/12/2014, 5:53:19 PM Β· Difficulty 10.9712 Β· 5,994,267 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cf9958b5638dbc4ed2444bc3e4dd93db882b617a7b05074bd724f8177dee8cbb
View on Chainz β†—

Height

#850,728

Difficulty

10.971169

Transactions

1

Size

207 B

Version

2

Bits

0af89e89

Nonce

2,131,503,125

Timestamp

12/12/2014, 5:53:19 PM

Confirmations

5,994,267

Merkle Root

4a51ba86e850a25e8f54d257b81877d75887d12a9429760d2e5ad4385ddaffae
Transactions (1)
Coinbase4a51ba86e850a2…5ad4385ddaffae
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.

1.486 Γ— 10⁹⁢(97-digit number)
14864518799025739936…86741747635423077520
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
1.486 Γ— 10⁹⁢(97-digit number)
14864518799025739936…86741747635423077521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.972 Γ— 10⁹⁢(97-digit number)
29729037598051479872…73483495270846155041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.945 Γ— 10⁹⁢(97-digit number)
59458075196102959744…46966990541692310081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.189 Γ— 10⁹⁷(98-digit number)
11891615039220591948…93933981083384620161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.378 Γ— 10⁹⁷(98-digit number)
23783230078441183897…87867962166769240321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.756 Γ— 10⁹⁷(98-digit number)
47566460156882367795…75735924333538480641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.513 Γ— 10⁹⁷(98-digit number)
95132920313764735591…51471848667076961281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.902 Γ— 10⁹⁸(99-digit number)
19026584062752947118…02943697334153922561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.805 Γ— 10⁹⁸(99-digit number)
38053168125505894236…05887394668307845121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.610 Γ— 10⁹⁸(99-digit number)
76106336251011788473…11774789336615690241
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 850728

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 cf9958b5638dbc4ed2444bc3e4dd93db882b617a7b05074bd724f8177dee8cbb

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 #850,728 on Chainz β†—
Circulating Supply:58,004,381 XPMΒ·at block #6,844,994 Β· updates every 60s
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