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Home/Chain Registry/Block #2,757,566

Block #2,757,566

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2018, 2:23:15 PM Β· Difficulty 11.6660 Β· 4,074,155 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d262f4902b705858f7ff06a475ddf747dc27fff422512a736d5328b3115eccf0
View on Chainz β†—

Difficulty

11.666023

Transactions

1

Size

200 B

Version

2

Bits

0baa807c

Nonce

859,252,525

Timestamp

7/20/2018, 2:23:15 PM

Confirmations

4,074,155

Merkle Root

bab6a878c9ef843dcaa7297343f7ed00e8c2eeb2a4df61c6d549eb005b7665ee
Transactions (1)
Coinbasebab6a878c9ef84…49eb005b7665ee
1 in β†’ 1 out7.3400 XPM110 B
AZtxQr2F…7grUWrUz
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.

8.036 Γ— 10⁹⁴(95-digit number)
80362260930821899060…12639904739923749170
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
8.036 Γ— 10⁹⁴(95-digit number)
80362260930821899060…12639904739923749169
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.607 Γ— 10⁹⁡(96-digit number)
16072452186164379812…25279809479847498339
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.214 Γ— 10⁹⁡(96-digit number)
32144904372328759624…50559618959694996679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.428 Γ— 10⁹⁡(96-digit number)
64289808744657519248…01119237919389993359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.285 Γ— 10⁹⁢(97-digit number)
12857961748931503849…02238475838779986719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.571 Γ— 10⁹⁢(97-digit number)
25715923497863007699…04476951677559973439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.143 Γ— 10⁹⁢(97-digit number)
51431846995726015398…08953903355119946879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.028 Γ— 10⁹⁷(98-digit number)
10286369399145203079…17907806710239893759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.057 Γ— 10⁹⁷(98-digit number)
20572738798290406159…35815613420479787519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.114 Γ— 10⁹⁷(98-digit number)
41145477596580812318…71631226840959575039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.229 Γ— 10⁹⁷(98-digit number)
82290955193161624637…43262453681919150079
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 2757566

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 d262f4902b705858f7ff06a475ddf747dc27fff422512a736d5328b3115eccf0

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 #2,757,566 on Chainz β†—
Circulating Supply:57,897,872 XPMΒ·at block #6,831,720 Β· updates every 60s
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