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Home/Chain Registry/Block #2,142,192

Block #2,142,192

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/2/2017, 6:16:44 PM Β· Difficulty 10.8745 Β· 4,689,171 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f8c475fc61744a926d8f77d68b58adc50b7c41c03920c6ee6691f1fbde288280
View on Chainz β†—

Difficulty

10.874480

Transactions

1

Size

199 B

Version

2

Bits

0adfddf3

Nonce

1,606,793,305

Timestamp

6/2/2017, 6:16:44 PM

Confirmations

4,689,171

Merkle Root

028556ec971de7870103d7f266b25001ed26ba6bc56916cf11c9b76c5ef2b86b
Transactions (1)
Coinbase028556ec971de7…c9b76c5ef2b86b
1 in β†’ 1 out8.4400 XPM109 B
AR6T64EE…DNvKv5Nb
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.

9.966 Γ— 10⁹³(94-digit number)
99660763525458197112…97884845930554495700
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
9.966 Γ— 10⁹³(94-digit number)
99660763525458197112…97884845930554495699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.993 Γ— 10⁹⁴(95-digit number)
19932152705091639422…95769691861108991399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.986 Γ— 10⁹⁴(95-digit number)
39864305410183278844…91539383722217982799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.972 Γ— 10⁹⁴(95-digit number)
79728610820366557689…83078767444435965599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.594 Γ— 10⁹⁡(96-digit number)
15945722164073311537…66157534888871931199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.189 Γ— 10⁹⁡(96-digit number)
31891444328146623075…32315069777743862399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.378 Γ— 10⁹⁡(96-digit number)
63782888656293246151…64630139555487724799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.275 Γ— 10⁹⁢(97-digit number)
12756577731258649230…29260279110975449599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.551 Γ— 10⁹⁢(97-digit number)
25513155462517298460…58520558221950899199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.102 Γ— 10⁹⁢(97-digit number)
51026310925034596921…17041116443901798399
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 2142192

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 f8c475fc61744a926d8f77d68b58adc50b7c41c03920c6ee6691f1fbde288280

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 #2,142,192 on Chainz β†—
Circulating Supply:57,895,059 XPMΒ·at block #6,831,362 Β· updates every 60s
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