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Home/Chain Registry/Block #2,916,854

Block #2,916,854

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/10/2018, 3:40:44 AM Β· Difficulty 11.4285 Β· 3,928,496 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dc3042173b07e8bba6edeeddf9ef4a7da0bf13fd1cbda60206ae6cd95bdc495c
View on Chainz β†—

Difficulty

11.428510

Transactions

1

Size

198 B

Version

2

Bits

0b6db2d3

Nonce

1,157,848,257

Timestamp

11/10/2018, 3:40:44 AM

Confirmations

3,928,496

Merkle Root

ad0f6d043851c261cd42caf8b82e52d1f33d2155df31c8c4850803235e9f3d4f
Transactions (1)
Coinbasead0f6d043851c2…0803235e9f3d4f
1 in β†’ 1 out7.6400 XPM109 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.

1.539 Γ— 10⁹³(94-digit number)
15394412624436931285…49862899525168974720
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
1.539 Γ— 10⁹³(94-digit number)
15394412624436931285…49862899525168974719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.078 Γ— 10⁹³(94-digit number)
30788825248873862570…99725799050337949439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.157 Γ— 10⁹³(94-digit number)
61577650497747725141…99451598100675898879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.231 Γ— 10⁹⁴(95-digit number)
12315530099549545028…98903196201351797759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.463 Γ— 10⁹⁴(95-digit number)
24631060199099090056…97806392402703595519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.926 Γ— 10⁹⁴(95-digit number)
49262120398198180113…95612784805407191039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.852 Γ— 10⁹⁴(95-digit number)
98524240796396360226…91225569610814382079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.970 Γ— 10⁹⁡(96-digit number)
19704848159279272045…82451139221628764159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.940 Γ— 10⁹⁡(96-digit number)
39409696318558544090…64902278443257528319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.881 Γ— 10⁹⁡(96-digit number)
78819392637117088181…29804556886515056639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.576 Γ— 10⁹⁢(97-digit number)
15763878527423417636…59609113773030113279
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 2916854

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 dc3042173b07e8bba6edeeddf9ef4a7da0bf13fd1cbda60206ae6cd95bdc495c

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 #2,916,854 on Chainz β†—
Circulating Supply:58,007,243 XPMΒ·at block #6,845,349 Β· updates every 60s
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