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Home/Chain Registry/Block #3,011,754

Block #3,011,754

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/16/2019, 8:33:52 AM Β· Difficulty 11.1762 Β· 3,831,228 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bdf33cc29166379136056a2717f5688a239757b98fbcd84817f73dc634307b8f
View on Chainz β†—

Difficulty

11.176206

Transactions

1

Size

200 B

Version

2

Bits

0b2d1bdc

Nonce

1,335,383,831

Timestamp

1/16/2019, 8:33:52 AM

Confirmations

3,831,228

Merkle Root

38ad0ce76020bd8c56ec1d6ceeceb07df57b9cbb32b6f85d68711a0b3cd466b4
Transactions (1)
Coinbase38ad0ce76020bd…711a0b3cd466b4
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.

5.931 Γ— 10⁹⁡(96-digit number)
59313010751798574458…50440307235656025600
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
5.931 Γ— 10⁹⁡(96-digit number)
59313010751798574458…50440307235656025599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.186 Γ— 10⁹⁢(97-digit number)
11862602150359714891…00880614471312051199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.372 Γ— 10⁹⁢(97-digit number)
23725204300719429783…01761228942624102399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.745 Γ— 10⁹⁢(97-digit number)
47450408601438859566…03522457885248204799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.490 Γ— 10⁹⁢(97-digit number)
94900817202877719133…07044915770496409599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.898 Γ— 10⁹⁷(98-digit number)
18980163440575543826…14089831540992819199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.796 Γ— 10⁹⁷(98-digit number)
37960326881151087653…28179663081985638399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.592 Γ— 10⁹⁷(98-digit number)
75920653762302175306…56359326163971276799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.518 Γ— 10⁹⁸(99-digit number)
15184130752460435061…12718652327942553599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.036 Γ— 10⁹⁸(99-digit number)
30368261504920870122…25437304655885107199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.073 Γ— 10⁹⁸(99-digit number)
60736523009841740245…50874609311770214399
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 3011754

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 bdf33cc29166379136056a2717f5688a239757b98fbcd84817f73dc634307b8f

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 #3,011,754 on Chainz β†—
Circulating Supply:57,988,211 XPMΒ·at block #6,842,981 Β· updates every 60s
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