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Home/Chain Registry/Block #2,150,286

Block #2,150,286

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/7/2017, 3:05:49 PM Β· Difficulty 10.8990 Β· 4,692,771 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8dbf4cdf8ffe6875d02e9141440f76246f6ef6024f1962cd0bfa24c2912d5553
View on Chainz β†—

Difficulty

10.899033

Transactions

2

Size

427 B

Version

2

Bits

0ae62703

Nonce

546,350,443

Timestamp

6/7/2017, 3:05:49 PM

Confirmations

4,692,771

Merkle Root

95899da22f89b1e3a45703cfda4802a00ef314fc3612c92c922eef6f7be4fc06
Transactions (2)
Coinbasec4dd58c7258053…50dbe1e31c8525
1 in β†’ 1 out8.4100 XPM110 B
ASBA1ksp…c9qMyhdN
66e0612fb9bdc5…65c045a0950526
1 in β†’ 2 out2588.8117 XPM227 B
AVgCRp5g…CqBzN8q8AYCJFQNZ…1MxxFDie
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.

2.253 Γ— 10⁹⁴(95-digit number)
22536130291898427553…15653949353852574880
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
2.253 Γ— 10⁹⁴(95-digit number)
22536130291898427553…15653949353852574879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.507 Γ— 10⁹⁴(95-digit number)
45072260583796855107…31307898707705149759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.014 Γ— 10⁹⁴(95-digit number)
90144521167593710215…62615797415410299519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.802 Γ— 10⁹⁡(96-digit number)
18028904233518742043…25231594830820599039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.605 Γ— 10⁹⁡(96-digit number)
36057808467037484086…50463189661641198079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.211 Γ— 10⁹⁡(96-digit number)
72115616934074968172…00926379323282396159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.442 Γ— 10⁹⁢(97-digit number)
14423123386814993634…01852758646564792319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.884 Γ— 10⁹⁢(97-digit number)
28846246773629987268…03705517293129584639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.769 Γ— 10⁹⁢(97-digit number)
57692493547259974537…07411034586259169279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.153 Γ— 10⁹⁷(98-digit number)
11538498709451994907…14822069172518338559
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 2150286

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 8dbf4cdf8ffe6875d02e9141440f76246f6ef6024f1962cd0bfa24c2912d5553

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 #2,150,286 on Chainz β†—
Circulating Supply:57,988,814 XPMΒ·at block #6,843,056 Β· updates every 60s
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