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Home/Chain Registry/Block #2,174,068

Block #2,174,068

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/23/2017, 5:39:04 PM Β· Difficulty 10.9108 Β· 4,665,183 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ebef05f469a86b2d8b3961e9bfd6cd9da7db4201976a1fe60c3b91c7ce4daa44
View on Chainz β†—

Difficulty

10.910829

Transactions

2

Size

5.30 KB

Version

2

Bits

0ae92c19

Nonce

1,611,580,453

Timestamp

6/23/2017, 5:39:04 PM

Confirmations

4,665,183

Merkle Root

87843e554a6a004c8d0413ab96b294c30d661aaae16ec7bf1ac3906e64ce0595
Transactions (2)
Coinbaseb3062513e3d010…8377c08c806e42
1 in β†’ 1 out8.4500 XPM109 B
APhYseJx…BXqpmqUq
35de022666dded…6b090236ff310a
35 in β†’ 1 out0.2900 XPM5.10 KB
AFqfQKkD…mrJU2vGS
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.

4.357 Γ— 10⁹⁴(95-digit number)
43578437716693509965…65172425884131099630
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
4.357 Γ— 10⁹⁴(95-digit number)
43578437716693509965…65172425884131099631
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.715 Γ— 10⁹⁴(95-digit number)
87156875433387019930…30344851768262199261
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.743 Γ— 10⁹⁡(96-digit number)
17431375086677403986…60689703536524398521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.486 Γ— 10⁹⁡(96-digit number)
34862750173354807972…21379407073048797041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.972 Γ— 10⁹⁡(96-digit number)
69725500346709615944…42758814146097594081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.394 Γ— 10⁹⁢(97-digit number)
13945100069341923188…85517628292195188161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.789 Γ— 10⁹⁢(97-digit number)
27890200138683846377…71035256584390376321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.578 Γ— 10⁹⁢(97-digit number)
55780400277367692755…42070513168780752641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.115 Γ— 10⁹⁷(98-digit number)
11156080055473538551…84141026337561505281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.231 Γ— 10⁹⁷(98-digit number)
22312160110947077102…68282052675123010561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.462 Γ— 10⁹⁷(98-digit number)
44624320221894154204…36564105350246021121
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2174068

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 ebef05f469a86b2d8b3961e9bfd6cd9da7db4201976a1fe60c3b91c7ce4daa44

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 #2,174,068 on Chainz β†—
Circulating Supply:57,958,291 XPMΒ·at block #6,839,250 Β· updates every 60s
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