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Home/Chain Registry/Block #3,054,792

Block #3,054,792

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/16/2019, 3:13:46 AM Β· Difficulty 11.0021 Β· 3,782,113 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4e9abb51c53ef0d063cfc0580c4ad72a65c54e642a2b97be0b416b687d9f3ba2
View on Chainz β†—

Difficulty

11.002054

Transactions

1

Size

200 B

Version

2

Bits

0b008697

Nonce

1,144,890,200

Timestamp

2/16/2019, 3:13:46 AM

Confirmations

3,782,113

Merkle Root

19afe0dbd45274fd34eb4048c0e8a7ee6fadd742c0d248ab69a76fa73282a655
Transactions (1)
Coinbase19afe0dbd45274…a76fa73282a655
1 in β†’ 1 out8.2500 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.

1.015 Γ— 10⁹⁴(95-digit number)
10159405257364103599…86851270713266934400
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
1.015 Γ— 10⁹⁴(95-digit number)
10159405257364103599…86851270713266934399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.031 Γ— 10⁹⁴(95-digit number)
20318810514728207198…73702541426533868799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.063 Γ— 10⁹⁴(95-digit number)
40637621029456414397…47405082853067737599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.127 Γ— 10⁹⁴(95-digit number)
81275242058912828795…94810165706135475199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.625 Γ— 10⁹⁡(96-digit number)
16255048411782565759…89620331412270950399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.251 Γ— 10⁹⁡(96-digit number)
32510096823565131518…79240662824541900799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.502 Γ— 10⁹⁡(96-digit number)
65020193647130263036…58481325649083801599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.300 Γ— 10⁹⁢(97-digit number)
13004038729426052607…16962651298167603199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.600 Γ— 10⁹⁢(97-digit number)
26008077458852105214…33925302596335206399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.201 Γ— 10⁹⁢(97-digit number)
52016154917704210429…67850605192670412799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.040 Γ— 10⁹⁷(98-digit number)
10403230983540842085…35701210385340825599
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 3054792

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 4e9abb51c53ef0d063cfc0580c4ad72a65c54e642a2b97be0b416b687d9f3ba2

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 #3,054,792 on Chainz β†—
Circulating Supply:57,939,532 XPMΒ·at block #6,836,904 Β· updates every 60s
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