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Block #3,011,737

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/16/2019, 8:18:15 AM Β· Difficulty 11.1759 Β· 3,829,883 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
51d21f3591f42d1c0539d74b87270b0c0212b034f584b9c753068f0f542ce23b
View on Chainz β†—

Difficulty

11.175898

Transactions

1

Size

199 B

Version

2

Bits

0b2d07a5

Nonce

920,765,032

Timestamp

1/16/2019, 8:18:15 AM

Confirmations

3,829,883

Merkle Root

e5d9d49deb93dbeb1246c78872f8ed52ee0972ecb3548a6286847e3968d2b6c3
Transactions (1)
Coinbasee5d9d49deb93db…847e3968d2b6c3
1 in β†’ 1 out7.9900 XPM110 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.

1.829 Γ— 10⁹²(93-digit number)
18296231875885431307…71263950965500101460
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
1.829 Γ— 10⁹²(93-digit number)
18296231875885431307…71263950965500101459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.659 Γ— 10⁹²(93-digit number)
36592463751770862614…42527901931000202919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.318 Γ— 10⁹²(93-digit number)
73184927503541725228…85055803862000405839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.463 Γ— 10⁹³(94-digit number)
14636985500708345045…70111607724000811679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.927 Γ— 10⁹³(94-digit number)
29273971001416690091…40223215448001623359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.854 Γ— 10⁹³(94-digit number)
58547942002833380182…80446430896003246719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.170 Γ— 10⁹⁴(95-digit number)
11709588400566676036…60892861792006493439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.341 Γ— 10⁹⁴(95-digit number)
23419176801133352073…21785723584012986879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.683 Γ— 10⁹⁴(95-digit number)
46838353602266704146…43571447168025973759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.367 Γ— 10⁹⁴(95-digit number)
93676707204533408292…87142894336051947519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.873 Γ— 10⁹⁡(96-digit number)
18735341440906681658…74285788672103895039
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 3011737

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 51d21f3591f42d1c0539d74b87270b0c0212b034f584b9c753068f0f542ce23b

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 #3,011,737 on Chainz β†—
Circulating Supply:57,977,342 XPMΒ·at block #6,841,619 Β· updates every 60s
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