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Home/Chain Registry/Block #2,868,757

Block #2,868,757

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/5/2018, 7:07:48 PM Β· Difficulty 11.6717 Β· 3,976,332 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
397627833a249febe835c4a43a858baf0c0f7ae3c56b17baeb5d2e37950fc477
View on Chainz β†—

Difficulty

11.671726

Transactions

1

Size

200 B

Version

2

Bits

0babf63d

Nonce

145,155,146

Timestamp

10/5/2018, 7:07:48 PM

Confirmations

3,976,332

Merkle Root

8f689683c4f734a3fbcfde78edf00706a93cf35fd69a97a0fe4cc47d165e5023
Transactions (1)
Coinbase8f689683c4f734…4cc47d165e5023
1 in β†’ 1 out7.3300 XPM110 B
AUMQRepm…tAfKmdW1
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.

3.978 Γ— 10⁹⁡(96-digit number)
39786801230359316912…19265092252559253120
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
3.978 Γ— 10⁹⁡(96-digit number)
39786801230359316912…19265092252559253121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.957 Γ— 10⁹⁡(96-digit number)
79573602460718633824…38530184505118506241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.591 Γ— 10⁹⁢(97-digit number)
15914720492143726764…77060369010237012481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.182 Γ— 10⁹⁢(97-digit number)
31829440984287453529…54120738020474024961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.365 Γ— 10⁹⁢(97-digit number)
63658881968574907059…08241476040948049921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.273 Γ— 10⁹⁷(98-digit number)
12731776393714981411…16482952081896099841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.546 Γ— 10⁹⁷(98-digit number)
25463552787429962823…32965904163792199681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.092 Γ— 10⁹⁷(98-digit number)
50927105574859925647…65931808327584399361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.018 Γ— 10⁹⁸(99-digit number)
10185421114971985129…31863616655168798721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.037 Γ— 10⁹⁸(99-digit number)
20370842229943970259…63727233310337597441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.074 Γ— 10⁹⁸(99-digit number)
40741684459887940518…27454466620675194881
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 2868757

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 397627833a249febe835c4a43a858baf0c0f7ae3c56b17baeb5d2e37950fc477

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 #2,868,757 on Chainz β†—
Circulating Supply:58,005,140 XPMΒ·at block #6,845,088 Β· updates every 60s
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