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Home/Chain Registry/Block #2,140,535

Block #2,140,535

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/1/2017, 1:51:18 PM Β· Difficulty 10.8756 Β· 4,692,820 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3fc365b656cf8395a277bbab75caa5854289fc1b6e5da23c9c30c8b5ecd2579f
View on Chainz β†—

Difficulty

10.875622

Transactions

1

Size

198 B

Version

2

Bits

0ae028c0

Nonce

417,441,890

Timestamp

6/1/2017, 1:51:18 PM

Confirmations

4,692,820

Merkle Root

853c2e3266e674d9c2919cbfcefd695efb0e021477e968f619829ec8ad56d1fb
Transactions (1)
Coinbase853c2e3266e674…829ec8ad56d1fb
1 in β†’ 1 out8.4400 XPM109 B
AGsHdBwX…3vCQEHtS
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.

2.303 Γ— 10⁹²(93-digit number)
23039745168736952704…66160445538877145360
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.303 Γ— 10⁹²(93-digit number)
23039745168736952704…66160445538877145361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.607 Γ— 10⁹²(93-digit number)
46079490337473905409…32320891077754290721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.215 Γ— 10⁹²(93-digit number)
92158980674947810819…64641782155508581441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.843 Γ— 10⁹³(94-digit number)
18431796134989562163…29283564311017162881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.686 Γ— 10⁹³(94-digit number)
36863592269979124327…58567128622034325761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.372 Γ— 10⁹³(94-digit number)
73727184539958248655…17134257244068651521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.474 Γ— 10⁹⁴(95-digit number)
14745436907991649731…34268514488137303041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.949 Γ— 10⁹⁴(95-digit number)
29490873815983299462…68537028976274606081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.898 Γ— 10⁹⁴(95-digit number)
58981747631966598924…37074057952549212161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.179 Γ— 10⁹⁡(96-digit number)
11796349526393319784…74148115905098424321
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2140535

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 3fc365b656cf8395a277bbab75caa5854289fc1b6e5da23c9c30c8b5ecd2579f

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 #2,140,535 on Chainz β†—
Circulating Supply:57,911,038 XPMΒ·at block #6,833,354 Β· updates every 60s
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