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Home/Chain Registry/Block #2,125,365

Block #2,125,365

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/20/2017, 12:58:17 PM Β· Difficulty 10.9186 Β· 4,708,500 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c924685435638c720452ac32b0d5b6060f16b9ab7e34771cae1f62c46ccb59d7
View on Chainz β†—

Difficulty

10.918604

Transactions

1

Size

200 B

Version

2

Bits

0aeb29a3

Nonce

801,023,934

Timestamp

5/20/2017, 12:58:17 PM

Confirmations

4,708,500

Merkle Root

734804e1087d02502bbdf1b0942275708c78d41401c3dd986ae70823477f9589
Transactions (1)
Coinbase734804e1087d02…e70823477f9589
1 in β†’ 1 out8.3700 XPM109 B
AdmNnytW…1AcRq5yo
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.

1.307 Γ— 10⁹⁢(97-digit number)
13073708074170262257…36538766625014860800
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
1.307 Γ— 10⁹⁢(97-digit number)
13073708074170262257…36538766625014860801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.614 Γ— 10⁹⁢(97-digit number)
26147416148340524515…73077533250029721601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.229 Γ— 10⁹⁢(97-digit number)
52294832296681049030…46155066500059443201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.045 Γ— 10⁹⁷(98-digit number)
10458966459336209806…92310133000118886401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.091 Γ— 10⁹⁷(98-digit number)
20917932918672419612…84620266000237772801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.183 Γ— 10⁹⁷(98-digit number)
41835865837344839224…69240532000475545601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.367 Γ— 10⁹⁷(98-digit number)
83671731674689678449…38481064000951091201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.673 Γ— 10⁹⁸(99-digit number)
16734346334937935689…76962128001902182401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.346 Γ— 10⁹⁸(99-digit number)
33468692669875871379…53924256003804364801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.693 Γ— 10⁹⁸(99-digit number)
66937385339751742759…07848512007608729601
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 2125365

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 c924685435638c720452ac32b0d5b6060f16b9ab7e34771cae1f62c46ccb59d7

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 #2,125,365 on Chainz β†—
Circulating Supply:57,915,150 XPMΒ·at block #6,833,864 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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