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Home/Chain Registry/Block #2,727,093

Block #2,727,093

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/29/2018, 7:29:23 PM Β· Difficulty 11.6271 Β· 4,118,092 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
34ae617fa4702fb6f896769bfc90ddba13ce15941dc2c945b0e38a7097ccfa9e
View on Chainz β†—

Difficulty

11.627121

Transactions

1

Size

200 B

Version

2

Bits

0ba08b03

Nonce

941,928,747

Timestamp

6/29/2018, 7:29:23 PM

Confirmations

4,118,092

Merkle Root

bcc0e7c6c6e1131d93284b086b6cdbcf4c6546f29f6fd491427802f7a0f26f6a
Transactions (1)
Coinbasebcc0e7c6c6e113…7802f7a0f26f6a
1 in β†’ 1 out7.3800 XPM110 B
AP7gC9Jd…kXsZasJt
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.

3.525 Γ— 10⁹³(94-digit number)
35254080854590480957…09811618671855878000
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
3.525 Γ— 10⁹³(94-digit number)
35254080854590480957…09811618671855877999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.050 Γ— 10⁹³(94-digit number)
70508161709180961915…19623237343711755999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.410 Γ— 10⁹⁴(95-digit number)
14101632341836192383…39246474687423511999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.820 Γ— 10⁹⁴(95-digit number)
28203264683672384766…78492949374847023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.640 Γ— 10⁹⁴(95-digit number)
56406529367344769532…56985898749694047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.128 Γ— 10⁹⁡(96-digit number)
11281305873468953906…13971797499388095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.256 Γ— 10⁹⁡(96-digit number)
22562611746937907812…27943594998776191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.512 Γ— 10⁹⁡(96-digit number)
45125223493875815625…55887189997552383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.025 Γ— 10⁹⁡(96-digit number)
90250446987751631251…11774379995104767999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.805 Γ— 10⁹⁢(97-digit number)
18050089397550326250…23548759990209535999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.610 Γ— 10⁹⁢(97-digit number)
36100178795100652500…47097519980419071999
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 2727093

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 34ae617fa4702fb6f896769bfc90ddba13ce15941dc2c945b0e38a7097ccfa9e

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 #2,727,093 on Chainz β†—
Circulating Supply:58,005,913 XPMΒ·at block #6,845,184 Β· updates every 60s
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