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Block #906,855

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/23/2015, 4:46:09 PM Β· Difficulty 10.9354 Β· 5,898,750 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4baa32f7e942fd4a5417ebfa1a7a344e2e476536814c21a45dfb16d8b671b500
View on Chainz β†—

Height

#906,855

Difficulty

10.935360

Transactions

1

Size

206 B

Version

2

Bits

0aef73bb

Nonce

1,283,653,095

Timestamp

1/23/2015, 4:46:09 PM

Confirmations

5,898,750

Merkle Root

c441d80364c4d25e7cd3dbb3fa646da36d8bbcc1fc60ed7541e5864fbab2ec33
Transactions (1)
Coinbasec441d80364c4d2…e5864fbab2ec33
1 in β†’ 1 out8.3500 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.

8.139 Γ— 10⁹⁴(95-digit number)
81392063152541840083…25798480325458061500
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
8.139 Γ— 10⁹⁴(95-digit number)
81392063152541840083…25798480325458061499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.627 Γ— 10⁹⁡(96-digit number)
16278412630508368016…51596960650916122999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.255 Γ— 10⁹⁡(96-digit number)
32556825261016736033…03193921301832245999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.511 Γ— 10⁹⁡(96-digit number)
65113650522033472066…06387842603664491999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.302 Γ— 10⁹⁢(97-digit number)
13022730104406694413…12775685207328983999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.604 Γ— 10⁹⁢(97-digit number)
26045460208813388826…25551370414657967999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.209 Γ— 10⁹⁢(97-digit number)
52090920417626777653…51102740829315935999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.041 Γ— 10⁹⁷(98-digit number)
10418184083525355530…02205481658631871999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.083 Γ— 10⁹⁷(98-digit number)
20836368167050711061…04410963317263743999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.167 Γ— 10⁹⁷(98-digit number)
41672736334101422122…08821926634527487999
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 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
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 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 906855

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 4baa32f7e942fd4a5417ebfa1a7a344e2e476536814c21a45dfb16d8b671b500

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 #906,855 on Chainz β†—
Circulating Supply:57,688,913 XPMΒ·at block #6,805,604 Β· updates every 60s
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