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Home/Chain Registry/Block #2,051,420

Block #2,051,420

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/3/2017, 12:33:44 PM Β· Difficulty 10.7136 Β· 4,792,349 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7ea2d8d68b6c79f95b5888bcf9120d4d7d441a774d04a67177da780144df95fc
View on Chainz β†—

Difficulty

10.713580

Transactions

1

Size

200 B

Version

2

Bits

0ab6ad32

Nonce

9,936,564

Timestamp

4/3/2017, 12:33:44 PM

Confirmations

4,792,349

Merkle Root

172c97b8ba398b10146b39da2bc57be34168f2c8ed7eecd66611d491eca5372f
Transactions (1)
Coinbase172c97b8ba398b…11d491eca5372f
1 in β†’ 1 out8.7000 XPM109 B
AMdAAedx…ahma8k1Y
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.

1.014 Γ— 10⁹⁷(98-digit number)
10144819488531055369…75238098583531786240
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
1.014 Γ— 10⁹⁷(98-digit number)
10144819488531055369…75238098583531786241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.028 Γ— 10⁹⁷(98-digit number)
20289638977062110739…50476197167063572481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.057 Γ— 10⁹⁷(98-digit number)
40579277954124221479…00952394334127144961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.115 Γ— 10⁹⁷(98-digit number)
81158555908248442958…01904788668254289921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.623 Γ— 10⁹⁸(99-digit number)
16231711181649688591…03809577336508579841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.246 Γ— 10⁹⁸(99-digit number)
32463422363299377183…07619154673017159681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.492 Γ— 10⁹⁸(99-digit number)
64926844726598754366…15238309346034319361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.298 Γ— 10⁹⁹(100-digit number)
12985368945319750873…30476618692068638721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.597 Γ— 10⁹⁹(100-digit number)
25970737890639501746…60953237384137277441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.194 Γ— 10⁹⁹(100-digit number)
51941475781279003493…21906474768274554881
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 2051420

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 7ea2d8d68b6c79f95b5888bcf9120d4d7d441a774d04a67177da780144df95fc

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 #2,051,420 on Chainz β†—
Circulating Supply:57,994,526 XPMΒ·at block #6,843,768 Β· updates every 60s
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