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Home/Chain Registry/Block #2,135,863

Block #2,135,863

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/28/2017, 3:04:39 PM Β· Difficulty 10.8982 Β· 4,706,020 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d2a8fc641f72b03c27293868e76bb4ebccea8643767203a41b6fb54c5a7d050d
View on Chainz β†—

Difficulty

10.898194

Transactions

1

Size

200 B

Version

2

Bits

0ae5f007

Nonce

300,644,530

Timestamp

5/28/2017, 3:04:39 PM

Confirmations

4,706,020

Merkle Root

d4e4aa27a383561375aee9eba6f579b541a375b306f6cf3d272e3b3638ab55dc
Transactions (1)
Coinbased4e4aa27a38356…2e3b3638ab55dc
1 in β†’ 1 out8.4100 XPM110 B
AKam3iSD…fSojMVX6
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.

5.140 Γ— 10⁹³(94-digit number)
51407064433142912816…99832890036022250590
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
5.140 Γ— 10⁹³(94-digit number)
51407064433142912816…99832890036022250589
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.028 Γ— 10⁹⁴(95-digit number)
10281412886628582563…99665780072044501179
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.056 Γ— 10⁹⁴(95-digit number)
20562825773257165126…99331560144089002359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.112 Γ— 10⁹⁴(95-digit number)
41125651546514330253…98663120288178004719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.225 Γ— 10⁹⁴(95-digit number)
82251303093028660506…97326240576356009439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.645 Γ— 10⁹⁡(96-digit number)
16450260618605732101…94652481152712018879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.290 Γ— 10⁹⁡(96-digit number)
32900521237211464202…89304962305424037759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.580 Γ— 10⁹⁡(96-digit number)
65801042474422928404…78609924610848075519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.316 Γ— 10⁹⁢(97-digit number)
13160208494884585680…57219849221696151039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.632 Γ— 10⁹⁢(97-digit number)
26320416989769171361…14439698443392302079
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 2135863

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 d2a8fc641f72b03c27293868e76bb4ebccea8643767203a41b6fb54c5a7d050d

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 #2,135,863 on Chainz β†—
Circulating Supply:57,979,440 XPMΒ·at block #6,841,882 Β· updates every 60s
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