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Home/Chain Registry/Block #2,657,986

Block #2,657,986

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/12/2018, 11:39:02 AM Β· Difficulty 11.6587 Β· 4,178,917 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ebf964016c239869c7cc38285dc1ca734d1facb2c1cd41e4d44ac127b4b1590c
View on Chainz β†—

Difficulty

11.658736

Transactions

1

Size

200 B

Version

2

Bits

0ba8a2ed

Nonce

613,208,649

Timestamp

5/12/2018, 11:39:02 AM

Confirmations

4,178,917

Merkle Root

c3f9fd6f40db3730e8ecbdae821bdc84e1679edff525a386504f28f4d9b90515
Transactions (1)
Coinbasec3f9fd6f40db37…4f28f4d9b90515
1 in β†’ 1 out7.3400 XPM110 B
Adqah8zh…1WwoHJ9t
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.

2.142 Γ— 10⁹⁴(95-digit number)
21421962617041411543…84112601600834892800
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.142 Γ— 10⁹⁴(95-digit number)
21421962617041411543…84112601600834892799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.284 Γ— 10⁹⁴(95-digit number)
42843925234082823086…68225203201669785599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.568 Γ— 10⁹⁴(95-digit number)
85687850468165646173…36450406403339571199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.713 Γ— 10⁹⁡(96-digit number)
17137570093633129234…72900812806679142399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.427 Γ— 10⁹⁡(96-digit number)
34275140187266258469…45801625613358284799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.855 Γ— 10⁹⁡(96-digit number)
68550280374532516938…91603251226716569599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.371 Γ— 10⁹⁢(97-digit number)
13710056074906503387…83206502453433139199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.742 Γ— 10⁹⁢(97-digit number)
27420112149813006775…66413004906866278399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.484 Γ— 10⁹⁢(97-digit number)
54840224299626013551…32826009813732556799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.096 Γ— 10⁹⁷(98-digit number)
10968044859925202710…65652019627465113599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.193 Γ— 10⁹⁷(98-digit number)
21936089719850405420…31304039254930227199
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2657986

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 ebf964016c239869c7cc38285dc1ca734d1facb2c1cd41e4d44ac127b4b1590c

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 #2,657,986 on Chainz β†—
Circulating Supply:57,939,516 XPMΒ·at block #6,836,902 Β· updates every 60s
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