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Block #855,047

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/16/2014, 1:42:51 AM Β· Difficulty 10.9685 Β· 5,976,099 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bfbe3c84cfcca81f740e58dfc111461905040d816ccf43bd53ce7b387412f475
View on Chainz β†—

Height

#855,047

Difficulty

10.968493

Transactions

1

Size

243 B

Version

2

Bits

0af7ef2c

Nonce

484,393,150

Timestamp

12/16/2014, 1:42:51 AM

Confirmations

5,976,099

Merkle Root

600fb11c6a72796eb427d1c90da07cc7c7c9cacf5c736d9b44a78003dfa00df3
Transactions (1)
Coinbase600fb11c6a7279…a78003dfa00df3
1 in β†’ 2 out8.3000 XPM152 B
AUV3ZXsa…P3xQCbyHALPu3s2c…EJXLjVFh
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.

4.249 Γ— 10⁹⁷(98-digit number)
42491318054754119837…81589973832269363200
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
4.249 Γ— 10⁹⁷(98-digit number)
42491318054754119837…81589973832269363201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.498 Γ— 10⁹⁷(98-digit number)
84982636109508239674…63179947664538726401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.699 Γ— 10⁹⁸(99-digit number)
16996527221901647934…26359895329077452801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.399 Γ— 10⁹⁸(99-digit number)
33993054443803295869…52719790658154905601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.798 Γ— 10⁹⁸(99-digit number)
67986108887606591739…05439581316309811201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.359 Γ— 10⁹⁹(100-digit number)
13597221777521318347…10879162632619622401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.719 Γ— 10⁹⁹(100-digit number)
27194443555042636695…21758325265239244801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.438 Γ— 10⁹⁹(100-digit number)
54388887110085273391…43516650530478489601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.087 Γ— 10¹⁰⁰(101-digit number)
10877777422017054678…87033301060956979201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.175 Γ— 10¹⁰⁰(101-digit number)
21755554844034109356…74066602121913958401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.351 Γ— 10¹⁰⁰(101-digit number)
43511109688068218713…48133204243827916801
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 855047

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 bfbe3c84cfcca81f740e58dfc111461905040d816ccf43bd53ce7b387412f475

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 #855,047 on Chainz β†—
Circulating Supply:57,893,306 XPMΒ·at block #6,831,145 Β· updates every 60s
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