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Home/Chain Registry/Block #2,139,010

Block #2,139,010

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/31/2017, 9:19:39 AM Β· Difficulty 10.8801 Β· 4,706,638 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
293e3dd696652e1cc076077d2aac6adce798b718a96728818ba92a63b15b69aa
View on Chainz β†—

Difficulty

10.880101

Transactions

1

Size

200 B

Version

2

Bits

0ae14e47

Nonce

326,432,796

Timestamp

5/31/2017, 9:19:39 AM

Confirmations

4,706,638

Merkle Root

33ef66a1c09a58c0acbf73b9881abfbc03bef6f93a90e6149d1fa1e7ad132246
Transactions (1)
Coinbase33ef66a1c09a58…1fa1e7ad132246
1 in β†’ 1 out8.4300 XPM110 B
AbLJfQnK…TVej61XW
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.

2.108 Γ— 10⁹⁴(95-digit number)
21082075868954674962…92440163572925290800
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
2.108 Γ— 10⁹⁴(95-digit number)
21082075868954674962…92440163572925290801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.216 Γ— 10⁹⁴(95-digit number)
42164151737909349924…84880327145850581601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.432 Γ— 10⁹⁴(95-digit number)
84328303475818699848…69760654291701163201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.686 Γ— 10⁹⁡(96-digit number)
16865660695163739969…39521308583402326401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.373 Γ— 10⁹⁡(96-digit number)
33731321390327479939…79042617166804652801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.746 Γ— 10⁹⁡(96-digit number)
67462642780654959878…58085234333609305601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.349 Γ— 10⁹⁢(97-digit number)
13492528556130991975…16170468667218611201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.698 Γ— 10⁹⁢(97-digit number)
26985057112261983951…32340937334437222401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.397 Γ— 10⁹⁢(97-digit number)
53970114224523967902…64681874668874444801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.079 Γ— 10⁹⁷(98-digit number)
10794022844904793580…29363749337748889601
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 2139010

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 293e3dd696652e1cc076077d2aac6adce798b718a96728818ba92a63b15b69aa

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 #2,139,010 on Chainz β†—
Circulating Supply:58,009,633 XPMΒ·at block #6,845,647 Β· updates every 60s
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