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Home/Chain Registry/Block #1,681,863

Block #1,681,863

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2016, 3:22:37 PM Β· Difficulty 10.7165 Β· 5,160,294 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
93c8d50641db6cc972b096647710406ec8d16624ad9e63fe1e7d01a30db39592
View on Chainz β†—

Difficulty

10.716512

Transactions

1

Size

200 B

Version

2

Bits

0ab76d50

Nonce

768,843,116

Timestamp

7/20/2016, 3:22:37 PM

Confirmations

5,160,294

Merkle Root

d1d5d9ae510a1a05e3d02e56bb2412726dd85be674a36b1280bbade9e4a93d58
Transactions (1)
Coinbased1d5d9ae510a1a…bbade9e4a93d58
1 in β†’ 1 out8.6900 XPM110 B
AJmV2hWg…3HuM6rLQ
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.

1.171 Γ— 10⁹⁡(96-digit number)
11715923126164102956…85638306006814546160
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
1.171 Γ— 10⁹⁡(96-digit number)
11715923126164102956…85638306006814546159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.343 Γ— 10⁹⁡(96-digit number)
23431846252328205912…71276612013629092319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.686 Γ— 10⁹⁡(96-digit number)
46863692504656411825…42553224027258184639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.372 Γ— 10⁹⁡(96-digit number)
93727385009312823651…85106448054516369279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.874 Γ— 10⁹⁢(97-digit number)
18745477001862564730…70212896109032738559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.749 Γ— 10⁹⁢(97-digit number)
37490954003725129460…40425792218065477119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.498 Γ— 10⁹⁢(97-digit number)
74981908007450258921…80851584436130954239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.499 Γ— 10⁹⁷(98-digit number)
14996381601490051784…61703168872261908479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.999 Γ— 10⁹⁷(98-digit number)
29992763202980103568…23406337744523816959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.998 Γ— 10⁹⁷(98-digit number)
59985526405960207137…46812675489047633919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.199 Γ— 10⁹⁸(99-digit number)
11997105281192041427…93625350978095267839
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 1681863

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 93c8d50641db6cc972b096647710406ec8d16624ad9e63fe1e7d01a30db39592

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 #1,681,863 on Chainz β†—
Circulating Supply:57,981,646 XPMΒ·at block #6,842,156 Β· updates every 60s
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