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Block #854,170

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/15/2014, 10:17:56 AM Β· Difficulty 10.9688 Β· 5,989,687 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
07941f2b22650b8634594938b4879cdf0719b24c4f2eb40a98629886c3c0da70
View on Chainz β†—

Height

#854,170

Difficulty

10.968764

Transactions

1

Size

207 B

Version

2

Bits

0af800f3

Nonce

1,953,467,654

Timestamp

12/15/2014, 10:17:56 AM

Confirmations

5,989,687

Merkle Root

0c794e9b327e02cc4d16a1d4ef9edcdf35d1f8f05816ccc1471d142c9e8f9994
Transactions (1)
Coinbase0c794e9b327e02…1d142c9e8f9994
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

2.406 Γ— 10⁹⁢(97-digit number)
24060673151175681309…42279189185132508480
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
2.406 Γ— 10⁹⁢(97-digit number)
24060673151175681309…42279189185132508481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.812 Γ— 10⁹⁢(97-digit number)
48121346302351362619…84558378370265016961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.624 Γ— 10⁹⁢(97-digit number)
96242692604702725239…69116756740530033921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.924 Γ— 10⁹⁷(98-digit number)
19248538520940545047…38233513481060067841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.849 Γ— 10⁹⁷(98-digit number)
38497077041881090095…76467026962120135681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.699 Γ— 10⁹⁷(98-digit number)
76994154083762180191…52934053924240271361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.539 Γ— 10⁹⁸(99-digit number)
15398830816752436038…05868107848480542721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.079 Γ— 10⁹⁸(99-digit number)
30797661633504872076…11736215696961085441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.159 Γ— 10⁹⁸(99-digit number)
61595323267009744153…23472431393922170881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.231 Γ— 10⁹⁹(100-digit number)
12319064653401948830…46944862787844341761
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 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
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 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 854170

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 07941f2b22650b8634594938b4879cdf0719b24c4f2eb40a98629886c3c0da70

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 #854,170 on Chainz β†—
Circulating Supply:57,995,224 XPMΒ·at block #6,843,856 Β· updates every 60s
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