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Home/Chain Registry/Block #3,334,757

Block #3,334,757

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/31/2019, 10:16:51 AM Β· Difficulty 10.9961 Β· 3,510,859 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2400180173b0c738cea57f42f4c8125f643881c57ff6567c047f3e7ca65f200c
View on Chainz β†—

Difficulty

10.996089

Transactions

1

Size

201 B

Version

2

Bits

0afeffac

Nonce

830,715,441

Timestamp

8/31/2019, 10:16:51 AM

Confirmations

3,510,859

Merkle Root

9ac64970aa6d5b61ddf8d5bed763f6cb840dca3f3d4efc66cff04e10a46cedfc
Transactions (1)
Coinbase9ac64970aa6d5b…f04e10a46cedfc
1 in β†’ 1 out8.2600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

6.740 Γ— 10⁹⁢(97-digit number)
67408410469147990782…57396057470838660800
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
6.740 Γ— 10⁹⁢(97-digit number)
67408410469147990782…57396057470838660799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.348 Γ— 10⁹⁷(98-digit number)
13481682093829598156…14792114941677321599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.696 Γ— 10⁹⁷(98-digit number)
26963364187659196312…29584229883354643199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.392 Γ— 10⁹⁷(98-digit number)
53926728375318392625…59168459766709286399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.078 Γ— 10⁹⁸(99-digit number)
10785345675063678525…18336919533418572799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.157 Γ— 10⁹⁸(99-digit number)
21570691350127357050…36673839066837145599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.314 Γ— 10⁹⁸(99-digit number)
43141382700254714100…73347678133674291199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.628 Γ— 10⁹⁸(99-digit number)
86282765400509428201…46695356267348582399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.725 Γ— 10⁹⁹(100-digit number)
17256553080101885640…93390712534697164799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.451 Γ— 10⁹⁹(100-digit number)
34513106160203771280…86781425069394329599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.902 Γ— 10⁹⁹(100-digit number)
69026212320407542560…73562850138788659199
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 3334757

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 2400180173b0c738cea57f42f4c8125f643881c57ff6567c047f3e7ca65f200c

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 #3,334,757 on Chainz β†—
Circulating Supply:58,009,374 XPMΒ·at block #6,845,615 Β· updates every 60s
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