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Home/Chain Registry/Block #2,166,778

Block #2,166,778

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/19/2017, 3:25:48 AM Β· Difficulty 10.8978 Β· 4,657,802 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
31916e46b6ed70a6f530329ae3cb928adcd5aec0014bdd92f7442938cd36ba7a
View on Chainz β†—

Difficulty

10.897778

Transactions

1

Size

200 B

Version

2

Bits

0ae5d4ca

Nonce

1,058,625,071

Timestamp

6/19/2017, 3:25:48 AM

Confirmations

4,657,802

Merkle Root

6b96f2c7a2c8285618e72844fa8f40d0a3c9ac4ca74838a3ef3df8f65a24b208
Transactions (1)
Coinbase6b96f2c7a2c828…3df8f65a24b208
1 in β†’ 1 out8.4100 XPM110 B
AXZiPF8b…BrE6rKVs
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.

7.595 Γ— 10⁹⁴(95-digit number)
75952206897629957317…93694437053934048080
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
7.595 Γ— 10⁹⁴(95-digit number)
75952206897629957317…93694437053934048079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.519 Γ— 10⁹⁡(96-digit number)
15190441379525991463…87388874107868096159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.038 Γ— 10⁹⁡(96-digit number)
30380882759051982927…74777748215736192319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.076 Γ— 10⁹⁡(96-digit number)
60761765518103965854…49555496431472384639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.215 Γ— 10⁹⁢(97-digit number)
12152353103620793170…99110992862944769279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.430 Γ— 10⁹⁢(97-digit number)
24304706207241586341…98221985725889538559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.860 Γ— 10⁹⁢(97-digit number)
48609412414483172683…96443971451779077119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.721 Γ— 10⁹⁢(97-digit number)
97218824828966345366…92887942903558154239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.944 Γ— 10⁹⁷(98-digit number)
19443764965793269073…85775885807116308479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.888 Γ— 10⁹⁷(98-digit number)
38887529931586538146…71551771614232616959
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 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
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 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 2166778

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 31916e46b6ed70a6f530329ae3cb928adcd5aec0014bdd92f7442938cd36ba7a

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 #2,166,778 on Chainz β†—
Circulating Supply:57,840,707 XPMΒ·at block #6,824,579 Β· updates every 60s
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