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Block #874,843

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/30/2014, 5:11:48 AM Β· Difficulty 10.9653 Β· 5,952,365 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
49f91f11f206bc5d6fc6fd4109172460e4cbc8247254a67505da39f97e1894c6
View on Chainz β†—

Height

#874,843

Difficulty

10.965285

Transactions

1

Size

206 B

Version

2

Bits

0af71cf2

Nonce

1,519,001,843

Timestamp

12/30/2014, 5:11:48 AM

Confirmations

5,952,365

Merkle Root

5d573f5d8b90d40f2d9e3126b49d79a65818964aabace31add0f4114bc0a3b18
Transactions (1)
Coinbase5d573f5d8b90d4…0f4114bc0a3b18
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.

5.475 Γ— 10⁹⁴(95-digit number)
54757788071639366905…71912176736180194480
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
5.475 Γ— 10⁹⁴(95-digit number)
54757788071639366905…71912176736180194479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.095 Γ— 10⁹⁡(96-digit number)
10951557614327873381…43824353472360388959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.190 Γ— 10⁹⁡(96-digit number)
21903115228655746762…87648706944720777919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.380 Γ— 10⁹⁡(96-digit number)
43806230457311493524…75297413889441555839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.761 Γ— 10⁹⁡(96-digit number)
87612460914622987048…50594827778883111679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.752 Γ— 10⁹⁢(97-digit number)
17522492182924597409…01189655557766223359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.504 Γ— 10⁹⁢(97-digit number)
35044984365849194819…02379311115532446719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.008 Γ— 10⁹⁢(97-digit number)
70089968731698389638…04758622231064893439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.401 Γ— 10⁹⁷(98-digit number)
14017993746339677927…09517244462129786879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.803 Γ— 10⁹⁷(98-digit number)
28035987492679355855…19034488924259573759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.607 Γ— 10⁹⁷(98-digit number)
56071974985358711710…38068977848519147519
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 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
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 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 874843

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 49f91f11f206bc5d6fc6fd4109172460e4cbc8247254a67505da39f97e1894c6

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 #874,843 on Chainz β†—
Circulating Supply:57,861,762 XPMΒ·at block #6,827,207 Β· updates every 60s
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