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Home/Chain Registry/Block #2,257,751

Block #2,257,751

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/18/2017, 8:18:54 PM Β· Difficulty 10.9520 Β· 4,579,181 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f1f6da2f701a52d7dbdaadf0034a303294cfc691cdaf71b4f741fceeb1fa00e0
View on Chainz β†—

Difficulty

10.951984

Transactions

1

Size

199 B

Version

2

Bits

0af3b53e

Nonce

1,421,472,907

Timestamp

8/18/2017, 8:18:54 PM

Confirmations

4,579,181

Merkle Root

7bb8f24433f5c0d6539726c016c8c7faec97b809a832ac4616f24264700c4d90
Transactions (1)
Coinbase7bb8f24433f5c0…f24264700c4d90
1 in β†’ 1 out8.3200 XPM110 B
ATMaeuQu…CoBD6cyQ
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.

2.950 Γ— 10⁹²(93-digit number)
29501756678769079478…30561068215371194520
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
2.950 Γ— 10⁹²(93-digit number)
29501756678769079478…30561068215371194519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.900 Γ— 10⁹²(93-digit number)
59003513357538158957…61122136430742389039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.180 Γ— 10⁹³(94-digit number)
11800702671507631791…22244272861484778079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.360 Γ— 10⁹³(94-digit number)
23601405343015263583…44488545722969556159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.720 Γ— 10⁹³(94-digit number)
47202810686030527166…88977091445939112319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.440 Γ— 10⁹³(94-digit number)
94405621372061054332…77954182891878224639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.888 Γ— 10⁹⁴(95-digit number)
18881124274412210866…55908365783756449279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.776 Γ— 10⁹⁴(95-digit number)
37762248548824421733…11816731567512898559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.552 Γ— 10⁹⁴(95-digit number)
75524497097648843466…23633463135025797119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.510 Γ— 10⁹⁡(96-digit number)
15104899419529768693…47266926270051594239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2257751

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 f1f6da2f701a52d7dbdaadf0034a303294cfc691cdaf71b4f741fceeb1fa00e0

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 #2,257,751 on Chainz β†—
Circulating Supply:57,939,753 XPMΒ·at block #6,836,931 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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