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Home/Chain Registry/Block #1,695,206

Block #1,695,206

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/30/2016, 8:52:42 AM Β· Difficulty 10.6771 Β· 5,146,337 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9616610beed3c2aade4a140eed4040c311675e89722529563d84ae3d3c463e46
View on Chainz β†—

Difficulty

10.677051

Transactions

1

Size

198 B

Version

2

Bits

0aad5330

Nonce

1,038,783,675

Timestamp

7/30/2016, 8:52:42 AM

Confirmations

5,146,337

Merkle Root

0dfe47a0e832fe536c5aff530eabd441930cdaa1870f1aedbabd851942a2f0de
Transactions (1)
Coinbase0dfe47a0e832fe…bd851942a2f0de
1 in β†’ 1 out8.7600 XPM109 B
ASc51SDA…VCJqE9z4
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.

5.664 Γ— 10⁹²(93-digit number)
56642530826205106265…78490495876160911200
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
5.664 Γ— 10⁹²(93-digit number)
56642530826205106265…78490495876160911199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.132 Γ— 10⁹³(94-digit number)
11328506165241021253…56980991752321822399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.265 Γ— 10⁹³(94-digit number)
22657012330482042506…13961983504643644799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.531 Γ— 10⁹³(94-digit number)
45314024660964085012…27923967009287289599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.062 Γ— 10⁹³(94-digit number)
90628049321928170024…55847934018574579199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.812 Γ— 10⁹⁴(95-digit number)
18125609864385634004…11695868037149158399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.625 Γ— 10⁹⁴(95-digit number)
36251219728771268009…23391736074298316799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.250 Γ— 10⁹⁴(95-digit number)
72502439457542536019…46783472148596633599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.450 Γ— 10⁹⁡(96-digit number)
14500487891508507203…93566944297193267199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.900 Γ— 10⁹⁡(96-digit number)
29000975783017014407…87133888594386534399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.800 Γ— 10⁹⁡(96-digit number)
58001951566034028815…74267777188773068799
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 1695206

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 9616610beed3c2aade4a140eed4040c311675e89722529563d84ae3d3c463e46

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 #1,695,206 on Chainz β†—
Circulating Supply:57,976,726 XPMΒ·at block #6,841,542 Β· updates every 60s
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