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Home/Chain Registry/Block #1,680,608

Block #1,680,608

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/19/2016, 8:45:30 PM Β· Difficulty 10.7086 Β· 5,160,048 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c7ee5490beff210f82187c0ccbf63a7c9ff118d78622738afa2af10a3ee3390f
View on Chainz β†—

Difficulty

10.708592

Transactions

1

Size

199 B

Version

2

Bits

0ab56641

Nonce

524,804,832

Timestamp

7/19/2016, 8:45:30 PM

Confirmations

5,160,048

Merkle Root

d9a1c1530d71344e34d26a15f4445cd4c5f05da031e261ac97edf4bc7042066c
Transactions (1)
Coinbased9a1c1530d7134…edf4bc7042066c
1 in β†’ 1 out8.7100 XPM109 B
AVXzZ7yc…CddVgmcb
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.

5.881 Γ— 10⁹⁴(95-digit number)
58812550635936364612…45974569892299605080
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
5.881 Γ— 10⁹⁴(95-digit number)
58812550635936364612…45974569892299605079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.176 Γ— 10⁹⁡(96-digit number)
11762510127187272922…91949139784599210159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.352 Γ— 10⁹⁡(96-digit number)
23525020254374545845…83898279569198420319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.705 Γ— 10⁹⁡(96-digit number)
47050040508749091690…67796559138396840639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.410 Γ— 10⁹⁡(96-digit number)
94100081017498183380…35593118276793681279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.882 Γ— 10⁹⁢(97-digit number)
18820016203499636676…71186236553587362559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.764 Γ— 10⁹⁢(97-digit number)
37640032406999273352…42372473107174725119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.528 Γ— 10⁹⁢(97-digit number)
75280064813998546704…84744946214349450239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.505 Γ— 10⁹⁷(98-digit number)
15056012962799709340…69489892428698900479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.011 Γ— 10⁹⁷(98-digit number)
30112025925599418681…38979784857397800959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.022 Γ— 10⁹⁷(98-digit number)
60224051851198837363…77959569714795601919
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 1680608

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 c7ee5490beff210f82187c0ccbf63a7c9ff118d78622738afa2af10a3ee3390f

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 #1,680,608 on Chainz β†—
Circulating Supply:57,969,591 XPMΒ·at block #6,840,655 Β· updates every 60s
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