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Block #851,737

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/13/2014, 1:01:58 PM Β· Difficulty 10.9704 Β· 5,992,329 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9cb53d92ee04e989ed44e33fe71e84154f3f364b49116d137f66b830fcdf4c22
View on Chainz β†—

Height

#851,737

Difficulty

10.970411

Transactions

2

Size

432 B

Version

2

Bits

0af86cdb

Nonce

2,285,056,896

Timestamp

12/13/2014, 1:01:58 PM

Confirmations

5,992,329

Merkle Root

39dceeadffa46814cffaeabe5059fd76f19dfd6683af0e5219dff56d6bc52724
Transactions (2)
Coinbased6aa5532c23ae9…5bfb3ea8219001
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
3bbc325a2ede3c…f4ce0e75a4c684
1 in β†’ 2 out4.2700 XPM226 B
AbFJHDk8…PBzZicHZAdzAVaSF…HZ3uhbEA
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.

2.166 Γ— 10⁹⁴(95-digit number)
21668561373030174341…56654576534327535140
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
2.166 Γ— 10⁹⁴(95-digit number)
21668561373030174341…56654576534327535139
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.333 Γ— 10⁹⁴(95-digit number)
43337122746060348683…13309153068655070279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.667 Γ— 10⁹⁴(95-digit number)
86674245492120697367…26618306137310140559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.733 Γ— 10⁹⁡(96-digit number)
17334849098424139473…53236612274620281119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.466 Γ— 10⁹⁡(96-digit number)
34669698196848278947…06473224549240562239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.933 Γ— 10⁹⁡(96-digit number)
69339396393696557894…12946449098481124479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.386 Γ— 10⁹⁢(97-digit number)
13867879278739311578…25892898196962248959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.773 Γ— 10⁹⁢(97-digit number)
27735758557478623157…51785796393924497919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.547 Γ— 10⁹⁢(97-digit number)
55471517114957246315…03571592787848995839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.109 Γ— 10⁹⁷(98-digit number)
11094303422991449263…07143185575697991679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.218 Γ— 10⁹⁷(98-digit number)
22188606845982898526…14286371151395983359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 851737

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 9cb53d92ee04e989ed44e33fe71e84154f3f364b49116d137f66b830fcdf4c22

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 #851,737 on Chainz β†—
Circulating Supply:57,996,901 XPMΒ·at block #6,844,065 Β· updates every 60s
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