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Home/Chain Registry/Block #2,657,113

Block #2,657,113

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/11/2018, 4:56:15 PM Β· Difficulty 11.6753 Β· 4,179,965 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6c614ab031686ce2b40c5a961b81d2992d3e1e6a01927fdd8e98b90f1b9c6886
View on Chainz β†—

Difficulty

11.675276

Transactions

1

Size

201 B

Version

2

Bits

0bacdeeb

Nonce

433,345,657

Timestamp

5/11/2018, 4:56:15 PM

Confirmations

4,179,965

Merkle Root

df771d310bd09f0f372816f97ed7da8be898d505d42a234b9b854230eb58bd97
Transactions (1)
Coinbasedf771d310bd09f…854230eb58bd97
1 in β†’ 1 out7.3200 XPM110 B
ATpwoGMf…TyogLF32
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.

1.013 Γ— 10⁹⁢(97-digit number)
10134035233577454394…60521357141039904640
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
1.013 Γ— 10⁹⁢(97-digit number)
10134035233577454394…60521357141039904641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.026 Γ— 10⁹⁢(97-digit number)
20268070467154908788…21042714282079809281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.053 Γ— 10⁹⁢(97-digit number)
40536140934309817577…42085428564159618561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.107 Γ— 10⁹⁢(97-digit number)
81072281868619635154…84170857128319237121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.621 Γ— 10⁹⁷(98-digit number)
16214456373723927030…68341714256638474241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.242 Γ— 10⁹⁷(98-digit number)
32428912747447854061…36683428513276948481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.485 Γ— 10⁹⁷(98-digit number)
64857825494895708123…73366857026553896961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.297 Γ— 10⁹⁸(99-digit number)
12971565098979141624…46733714053107793921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.594 Γ— 10⁹⁸(99-digit number)
25943130197958283249…93467428106215587841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.188 Γ— 10⁹⁸(99-digit number)
51886260395916566498…86934856212431175681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.037 Γ— 10⁹⁹(100-digit number)
10377252079183313299…73869712424862351361
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 2657113

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 6c614ab031686ce2b40c5a961b81d2992d3e1e6a01927fdd8e98b90f1b9c6886

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 #2,657,113 on Chainz β†—
Circulating Supply:57,940,927 XPMΒ·at block #6,837,077 Β· updates every 60s
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