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Home/Chain Registry/Block #2,732,671

Block #2,732,671

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/3/2018, 3:26:15 PM Β· Difficulty 11.6317 Β· 4,108,717 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f2155126e01f23e50d1b0cc8deaf31fc069af40e4199b5a3ada4364af5eb1690
View on Chainz β†—

Difficulty

11.631744

Transactions

1

Size

201 B

Version

2

Bits

0ba1b9fc

Nonce

830,212,179

Timestamp

7/3/2018, 3:26:15 PM

Confirmations

4,108,717

Merkle Root

b279393fd1fa48ae9197c9aa549ba7ce0cb578959cc29b780efb905ab3591cbd
Transactions (1)
Coinbaseb279393fd1fa48…fb905ab3591cbd
1 in β†’ 1 out7.3800 XPM110 B
AeoazQjU…84PgS8bs
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.

1.254 Γ— 10⁹⁢(97-digit number)
12545440379204942103…40261982928041708800
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
1.254 Γ— 10⁹⁢(97-digit number)
12545440379204942103…40261982928041708799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.509 Γ— 10⁹⁢(97-digit number)
25090880758409884206…80523965856083417599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.018 Γ— 10⁹⁢(97-digit number)
50181761516819768412…61047931712166835199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.003 Γ— 10⁹⁷(98-digit number)
10036352303363953682…22095863424333670399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.007 Γ— 10⁹⁷(98-digit number)
20072704606727907364…44191726848667340799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.014 Γ— 10⁹⁷(98-digit number)
40145409213455814729…88383453697334681599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.029 Γ— 10⁹⁷(98-digit number)
80290818426911629459…76766907394669363199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.605 Γ— 10⁹⁸(99-digit number)
16058163685382325891…53533814789338726399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.211 Γ— 10⁹⁸(99-digit number)
32116327370764651783…07067629578677452799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.423 Γ— 10⁹⁸(99-digit number)
64232654741529303567…14135259157354905599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.284 Γ— 10⁹⁹(100-digit number)
12846530948305860713…28270518314709811199
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 2732671

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 f2155126e01f23e50d1b0cc8deaf31fc069af40e4199b5a3ada4364af5eb1690

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 #2,732,671 on Chainz β†—
Circulating Supply:57,975,475 XPMΒ·at block #6,841,387 Β· updates every 60s
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