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Home/Chain Registry/Block #2,076,268

Block #2,076,268

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/18/2017, 3:23:58 PM Β· Difficulty 10.8455 Β· 4,760,539 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9abcfdd4397a9fda807431f0aca01f27f44f30fe680a11d8f7eea1f3f8119c53
View on Chainz β†—

Difficulty

10.845492

Transactions

2

Size

1017 B

Version

2

Bits

0ad87222

Nonce

171,201,776

Timestamp

4/18/2017, 3:23:58 PM

Confirmations

4,760,539

Merkle Root

0ea069ba7cc895aaa4840f0a45e74f0f51a9a510c15ec69fda5bd3973a80b2f2
Transactions (2)
Coinbasee3f03623e183b8…98ecabafe98ca1
1 in β†’ 1 out8.5100 XPM109 B
AHbfzXG4…BmQYrT7Y
808e6cf681330b…69f45b1625ab47
5 in β†’ 2 out2404.1107 XPM818 B
AHKEqLWG…Z6JsKv41AY4wgKVp…ySbs5VYd
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.

1.093 Γ— 10⁹⁴(95-digit number)
10937560052118303515…32609099497456007420
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
1.093 Γ— 10⁹⁴(95-digit number)
10937560052118303515…32609099497456007419
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.187 Γ— 10⁹⁴(95-digit number)
21875120104236607030…65218198994912014839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.375 Γ— 10⁹⁴(95-digit number)
43750240208473214060…30436397989824029679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.750 Γ— 10⁹⁴(95-digit number)
87500480416946428120…60872795979648059359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.750 Γ— 10⁹⁡(96-digit number)
17500096083389285624…21745591959296118719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.500 Γ— 10⁹⁡(96-digit number)
35000192166778571248…43491183918592237439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.000 Γ— 10⁹⁡(96-digit number)
70000384333557142496…86982367837184474879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.400 Γ— 10⁹⁢(97-digit number)
14000076866711428499…73964735674368949759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.800 Γ— 10⁹⁢(97-digit number)
28000153733422856998…47929471348737899519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.600 Γ— 10⁹⁢(97-digit number)
56000307466845713997…95858942697475799039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.120 Γ— 10⁹⁷(98-digit number)
11200061493369142799…91717885394951598079
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 2076268

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 9abcfdd4397a9fda807431f0aca01f27f44f30fe680a11d8f7eea1f3f8119c53

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 #2,076,268 on Chainz β†—
Circulating Supply:57,938,739 XPMΒ·at block #6,836,806 Β· updates every 60s
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