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Block #857,002

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/17/2014, 12:43:24 PM Β· Difficulty 10.9676 Β· 5,986,118 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
34aa53b0a4f130a1906a59e0f9cb35a48010adfd4f89eb8e3b72e6c7edac2ae1
View on Chainz β†—

Height

#857,002

Difficulty

10.967629

Transactions

1

Size

207 B

Version

2

Bits

0af7b686

Nonce

966,571,066

Timestamp

12/17/2014, 12:43:24 PM

Confirmations

5,986,118

Merkle Root

e2834b7476b6da02c8313890c64cc19faa0f2856b4346eeed80fce5f552a2e28
Transactions (1)
Coinbasee2834b7476b6da…0fce5f552a2e28
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.

3.347 Γ— 10⁹⁢(97-digit number)
33479734751200176942…64203533728919440000
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
3.347 Γ— 10⁹⁢(97-digit number)
33479734751200176942…64203533728919439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.695 Γ— 10⁹⁢(97-digit number)
66959469502400353884…28407067457838879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.339 Γ— 10⁹⁷(98-digit number)
13391893900480070776…56814134915677759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.678 Γ— 10⁹⁷(98-digit number)
26783787800960141553…13628269831355519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.356 Γ— 10⁹⁷(98-digit number)
53567575601920283107…27256539662711039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.071 Γ— 10⁹⁸(99-digit number)
10713515120384056621…54513079325422079999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.142 Γ— 10⁹⁸(99-digit number)
21427030240768113242…09026158650844159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.285 Γ— 10⁹⁸(99-digit number)
42854060481536226485…18052317301688319999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.570 Γ— 10⁹⁸(99-digit number)
85708120963072452971…36104634603376639999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.714 Γ— 10⁹⁹(100-digit number)
17141624192614490594…72209269206753279999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.428 Γ— 10⁹⁹(100-digit number)
34283248385228981188…44418538413506559999
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 857002

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 34aa53b0a4f130a1906a59e0f9cb35a48010adfd4f89eb8e3b72e6c7edac2ae1

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 #857,002 on Chainz β†—
Circulating Supply:57,989,325 XPMΒ·at block #6,843,119 Β· updates every 60s
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