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Home/Chain Registry/Block #2,154,318

Block #2,154,318

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/10/2017, 6:11:27 AM Β· Difficulty 10.9040 Β· 4,687,552 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1be9f2568adf034d79cf2d7cdd4b7efdf7374a6cb54aed0c84cb0cafd8cb1b19
View on Chainz β†—

Difficulty

10.903958

Transactions

1

Size

200 B

Version

2

Bits

0ae769d1

Nonce

1,136,805,692

Timestamp

6/10/2017, 6:11:27 AM

Confirmations

4,687,552

Merkle Root

a5b26fc30949bf51f62dff5393a0b7f5293929e778334ec2a138cbf5b3e8f807
Transactions (1)
Coinbasea5b26fc30949bf…38cbf5b3e8f807
1 in β†’ 1 out8.4000 XPM109 B
AcXBskxa…rgBFjzBq
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.

1.699 Γ— 10⁹⁢(97-digit number)
16994623781867391854…53571775145125656320
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
1.699 Γ— 10⁹⁢(97-digit number)
16994623781867391854…53571775145125656319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.398 Γ— 10⁹⁢(97-digit number)
33989247563734783708…07143550290251312639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.797 Γ— 10⁹⁢(97-digit number)
67978495127469567417…14287100580502625279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.359 Γ— 10⁹⁷(98-digit number)
13595699025493913483…28574201161005250559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.719 Γ— 10⁹⁷(98-digit number)
27191398050987826967…57148402322010501119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.438 Γ— 10⁹⁷(98-digit number)
54382796101975653934…14296804644021002239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.087 Γ— 10⁹⁸(99-digit number)
10876559220395130786…28593609288042004479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.175 Γ— 10⁹⁸(99-digit number)
21753118440790261573…57187218576084008959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.350 Γ— 10⁹⁸(99-digit number)
43506236881580523147…14374437152168017919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.701 Γ— 10⁹⁸(99-digit number)
87012473763161046294…28748874304336035839
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 2154318

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 1be9f2568adf034d79cf2d7cdd4b7efdf7374a6cb54aed0c84cb0cafd8cb1b19

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 #2,154,318 on Chainz β†—
Circulating Supply:57,979,337 XPMΒ·at block #6,841,869 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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