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Home/Chain Registry/Block #2,931,172

Block #2,931,172

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/20/2018, 7:22:29 AM Β· Difficulty 11.3935 Β· 3,911,204 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a13800b63bae2d44ac6eca1986cee2d303747d35ec3df7c3127e0d311c89755f
View on Chainz β†—

Difficulty

11.393525

Transactions

1

Size

200 B

Version

2

Bits

0b64be14

Nonce

687,626,094

Timestamp

11/20/2018, 7:22:29 AM

Confirmations

3,911,204

Merkle Root

49d8c4b9d34387e9f9022768088b75a6bdf82f7718cfeb34245b673ea171fd0c
Transactions (1)
Coinbase49d8c4b9d34387…5b673ea171fd0c
1 in β†’ 1 out7.6900 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.

1.825 Γ— 10⁹⁴(95-digit number)
18255028006852673729…45221475789754548000
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
1.825 Γ— 10⁹⁴(95-digit number)
18255028006852673729…45221475789754547999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.651 Γ— 10⁹⁴(95-digit number)
36510056013705347459…90442951579509095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.302 Γ— 10⁹⁴(95-digit number)
73020112027410694918…80885903159018191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.460 Γ— 10⁹⁡(96-digit number)
14604022405482138983…61771806318036383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.920 Γ— 10⁹⁡(96-digit number)
29208044810964277967…23543612636072767999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.841 Γ— 10⁹⁡(96-digit number)
58416089621928555934…47087225272145535999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.168 Γ— 10⁹⁢(97-digit number)
11683217924385711186…94174450544291071999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.336 Γ— 10⁹⁢(97-digit number)
23366435848771422373…88348901088582143999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.673 Γ— 10⁹⁢(97-digit number)
46732871697542844747…76697802177164287999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.346 Γ— 10⁹⁢(97-digit number)
93465743395085689495…53395604354328575999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.869 Γ— 10⁹⁷(98-digit number)
18693148679017137899…06791208708657151999
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 2931172

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 a13800b63bae2d44ac6eca1986cee2d303747d35ec3df7c3127e0d311c89755f

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 #2,931,172 on Chainz β†—
Circulating Supply:57,983,417 XPMΒ·at block #6,842,375 Β· updates every 60s
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