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Home/Chain Registry/Block #3,113,976

Block #3,113,976

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/28/2019, 12:52:49 PM Β· Difficulty 11.2377 Β· 3,712,890 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
10c2f7b86c677fc7f042ea60aed7290707b6b6cc206b4715c8be1f33a9fbec47
View on Chainz β†—

Difficulty

11.237745

Transactions

1

Size

201 B

Version

2

Bits

0b3cdce0

Nonce

2,001,878,258

Timestamp

3/28/2019, 12:52:49 PM

Confirmations

3,712,890

Merkle Root

bf471fdad62db04879df8995dd6c71541754b87ba495494630bc40f8e57dcee7
Transactions (1)
Coinbasebf471fdad62db0…bc40f8e57dcee7
1 in β†’ 1 out7.9100 XPM110 B
AbXwmGxD…4XXYP765
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.

1.863 Γ— 10⁹⁢(97-digit number)
18635952640513767888…72499585644676531520
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
1.863 Γ— 10⁹⁢(97-digit number)
18635952640513767888…72499585644676531519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.727 Γ— 10⁹⁢(97-digit number)
37271905281027535776…44999171289353063039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.454 Γ— 10⁹⁢(97-digit number)
74543810562055071553…89998342578706126079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.490 Γ— 10⁹⁷(98-digit number)
14908762112411014310…79996685157412252159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.981 Γ— 10⁹⁷(98-digit number)
29817524224822028621…59993370314824504319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.963 Γ— 10⁹⁷(98-digit number)
59635048449644057242…19986740629649008639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.192 Γ— 10⁹⁸(99-digit number)
11927009689928811448…39973481259298017279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.385 Γ— 10⁹⁸(99-digit number)
23854019379857622897…79946962518596034559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.770 Γ— 10⁹⁸(99-digit number)
47708038759715245794…59893925037192069119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.541 Γ— 10⁹⁸(99-digit number)
95416077519430491588…19787850074384138239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.908 Γ— 10⁹⁹(100-digit number)
19083215503886098317…39575700148768276479
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 3113976

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 10c2f7b86c677fc7f042ea60aed7290707b6b6cc206b4715c8be1f33a9fbec47

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 #3,113,976 on Chainz β†—
Circulating Supply:57,859,090 XPMΒ·at block #6,826,865 Β· updates every 60s
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