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Home/Chain Registry/Block #2,247,678

Block #2,247,678

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/12/2017, 2:58:56 AM Β· Difficulty 10.9478 Β· 4,596,327 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
779b9f4cf66005e6513eaf4d22c11bc60e8d86f569f62f7fd5003ecfd6a6772e
View on Chainz β†—

Difficulty

10.947775

Transactions

1

Size

199 B

Version

2

Bits

0af2a165

Nonce

144,070,355

Timestamp

8/12/2017, 2:58:56 AM

Confirmations

4,596,327

Merkle Root

299ed51fad2c7d84086fb95c84c292d5b0bce0ee143b140d227d671460141f33
Transactions (1)
Coinbase299ed51fad2c7d…7d671460141f33
1 in β†’ 1 out8.3300 XPM109 B
AJkotwQM…NZqbmPYj
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.

1.857 Γ— 10⁹⁡(96-digit number)
18577678090475390250…57590464522493508160
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
1.857 Γ— 10⁹⁡(96-digit number)
18577678090475390250…57590464522493508161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.715 Γ— 10⁹⁡(96-digit number)
37155356180950780501…15180929044987016321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.431 Γ— 10⁹⁡(96-digit number)
74310712361901561002…30361858089974032641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.486 Γ— 10⁹⁢(97-digit number)
14862142472380312200…60723716179948065281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.972 Γ— 10⁹⁢(97-digit number)
29724284944760624401…21447432359896130561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.944 Γ— 10⁹⁢(97-digit number)
59448569889521248802…42894864719792261121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.188 Γ— 10⁹⁷(98-digit number)
11889713977904249760…85789729439584522241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.377 Γ— 10⁹⁷(98-digit number)
23779427955808499520…71579458879169044481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.755 Γ— 10⁹⁷(98-digit number)
47558855911616999041…43158917758338088961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.511 Γ— 10⁹⁷(98-digit number)
95117711823233998083…86317835516676177921
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 2247678

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 779b9f4cf66005e6513eaf4d22c11bc60e8d86f569f62f7fd5003ecfd6a6772e

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 #2,247,678 on Chainz β†—
Circulating Supply:57,996,421 XPMΒ·at block #6,844,004 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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