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Home/Chain Registry/Block #3,011,739

Block #3,011,739

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/16/2019, 8:19:05 AM Β· Difficulty 11.1760 Β· 3,832,259 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
264971e8618828426473b4e6f541ec836f33d98978d5658f05f8dc33eed796ed
View on Chainz β†—

Difficulty

11.175999

Transactions

1

Size

200 B

Version

2

Bits

0b2d0e42

Nonce

603,161,613

Timestamp

1/16/2019, 8:19:05 AM

Confirmations

3,832,259

Merkle Root

2c4ea9708fc20bd32e34a12670abc5c724147c67ed65421a481176c380b100da
Transactions (1)
Coinbase2c4ea9708fc20b…1176c380b100da
1 in β†’ 1 out7.9900 XPM109 B
AUhjokok…k5m93PZR
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.

3.221 Γ— 10⁹⁢(97-digit number)
32214760265872806095…63575975493871661760
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
3.221 Γ— 10⁹⁢(97-digit number)
32214760265872806095…63575975493871661759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.442 Γ— 10⁹⁢(97-digit number)
64429520531745612190…27151950987743323519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.288 Γ— 10⁹⁷(98-digit number)
12885904106349122438…54303901975486647039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.577 Γ— 10⁹⁷(98-digit number)
25771808212698244876…08607803950973294079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.154 Γ— 10⁹⁷(98-digit number)
51543616425396489752…17215607901946588159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.030 Γ— 10⁹⁸(99-digit number)
10308723285079297950…34431215803893176319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.061 Γ— 10⁹⁸(99-digit number)
20617446570158595900…68862431607786352639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.123 Γ— 10⁹⁸(99-digit number)
41234893140317191801…37724863215572705279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.246 Γ— 10⁹⁸(99-digit number)
82469786280634383603…75449726431145410559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.649 Γ— 10⁹⁹(100-digit number)
16493957256126876720…50899452862290821119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.298 Γ— 10⁹⁹(100-digit number)
32987914512253753441…01798905724581642239
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 3011739

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 264971e8618828426473b4e6f541ec836f33d98978d5658f05f8dc33eed796ed

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 #3,011,739 on Chainz β†—
Circulating Supply:57,996,365 XPMΒ·at block #6,843,997 Β· updates every 60s
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