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Home/Chain Registry/Block #2,179,235

Block #2,179,235

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/26/2017, 1:17:24 PM Β· Difficulty 10.9286 Β· 4,664,445 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
418e63f70f98579dc304d90643b0ba796d0b9b6763474dd6cf3a9fd2b388fd6c
View on Chainz β†—

Difficulty

10.928572

Transactions

1

Size

200 B

Version

2

Bits

0aedb6e0

Nonce

113,496,216

Timestamp

6/26/2017, 1:17:24 PM

Confirmations

4,664,445

Merkle Root

91683af93a8cf4abfd14590a880715822a71c661512ad5220872270741cde510
Transactions (1)
Coinbase91683af93a8cf4…72270741cde510
1 in β†’ 1 out8.3600 XPM109 B
AJzWVU7H…pwupts7Z
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.

1.586 Γ— 10⁹⁷(98-digit number)
15862750089782659614…32586614514390671360
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
1.586 Γ— 10⁹⁷(98-digit number)
15862750089782659614…32586614514390671361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.172 Γ— 10⁹⁷(98-digit number)
31725500179565319229…65173229028781342721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.345 Γ— 10⁹⁷(98-digit number)
63451000359130638459…30346458057562685441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.269 Γ— 10⁹⁸(99-digit number)
12690200071826127691…60692916115125370881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.538 Γ— 10⁹⁸(99-digit number)
25380400143652255383…21385832230250741761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.076 Γ— 10⁹⁸(99-digit number)
50760800287304510767…42771664460501483521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.015 Γ— 10⁹⁹(100-digit number)
10152160057460902153…85543328921002967041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.030 Γ— 10⁹⁹(100-digit number)
20304320114921804306…71086657842005934081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.060 Γ— 10⁹⁹(100-digit number)
40608640229843608613…42173315684011868161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.121 Γ— 10⁹⁹(100-digit number)
81217280459687217227…84346631368023736321
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 2179235

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 418e63f70f98579dc304d90643b0ba796d0b9b6763474dd6cf3a9fd2b388fd6c

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 #2,179,235 on Chainz β†—
Circulating Supply:57,993,813 XPMΒ·at block #6,843,679 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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