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Block #850,139

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/12/2014, 7:33:23 AM Β· Difficulty 10.9713 Β· 5,991,694 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
273e820185da7984dca0f4210b27342a765528de3c893ad8d8fbd451fc17fab2
View on Chainz β†—

Height

#850,139

Difficulty

10.971341

Transactions

2

Size

433 B

Version

2

Bits

0af8a9d6

Nonce

1,365,717,240

Timestamp

12/12/2014, 7:33:23 AM

Confirmations

5,991,694

Merkle Root

288f569a40f80b2e0630db90aabe58dfd44986f70decfef0e35bcad2141cfea5
Transactions (2)
Coinbase609cbc3a2b7053…96662439b3a137
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
70d56f81c8ebd3…9da8c31dcc100b
1 in β†’ 2 out0.1048 XPM226 B
Aad4xRGd…uT2R3eUwATgZk84C…CrwuJV2r
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.

3.882 Γ— 10⁹⁢(97-digit number)
38826893538019484367…81741461032844966560
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
3.882 Γ— 10⁹⁢(97-digit number)
38826893538019484367…81741461032844966561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.765 Γ— 10⁹⁢(97-digit number)
77653787076038968734…63482922065689933121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.553 Γ— 10⁹⁷(98-digit number)
15530757415207793746…26965844131379866241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.106 Γ— 10⁹⁷(98-digit number)
31061514830415587493…53931688262759732481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.212 Γ— 10⁹⁷(98-digit number)
62123029660831174987…07863376525519464961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.242 Γ— 10⁹⁸(99-digit number)
12424605932166234997…15726753051038929921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.484 Γ— 10⁹⁸(99-digit number)
24849211864332469995…31453506102077859841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.969 Γ— 10⁹⁸(99-digit number)
49698423728664939990…62907012204155719681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.939 Γ— 10⁹⁸(99-digit number)
99396847457329879980…25814024408311439361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.987 Γ— 10⁹⁹(100-digit number)
19879369491465975996…51628048816622878721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.975 Γ— 10⁹⁹(100-digit number)
39758738982931951992…03256097633245757441
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 850139

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 273e820185da7984dca0f4210b27342a765528de3c893ad8d8fbd451fc17fab2

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 #850,139 on Chainz β†—
Circulating Supply:57,979,037 XPMΒ·at block #6,841,832 Β· updates every 60s
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