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Block #956,682

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/1/2015, 5:27:47 AM Β· Difficulty 10.8904 Β· 5,870,325 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8f551cd52194e775a5b8e0628b3a2011d5c6b8b72963032be412b4a4f84f9bf4
View on Chainz β†—

Height

#956,682

Difficulty

10.890401

Transactions

1

Size

207 B

Version

2

Bits

0ae3f151

Nonce

723,169,626

Timestamp

3/1/2015, 5:27:47 AM

Confirmations

5,870,325

Merkle Root

dce9fff04792f549e1c209047d3a0c789c1d45cdac429d7047efbba8ed4a0024
Transactions (1)
Coinbasedce9fff04792f5…efbba8ed4a0024
1 in β†’ 1 out8.4200 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.

4.122 Γ— 10⁹⁢(97-digit number)
41228056311998286957…99900193379703219840
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
4.122 Γ— 10⁹⁢(97-digit number)
41228056311998286957…99900193379703219839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.245 Γ— 10⁹⁢(97-digit number)
82456112623996573914…99800386759406439679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.649 Γ— 10⁹⁷(98-digit number)
16491222524799314782…99600773518812879359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.298 Γ— 10⁹⁷(98-digit number)
32982445049598629565…99201547037625758719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.596 Γ— 10⁹⁷(98-digit number)
65964890099197259131…98403094075251517439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.319 Γ— 10⁹⁸(99-digit number)
13192978019839451826…96806188150503034879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.638 Γ— 10⁹⁸(99-digit number)
26385956039678903652…93612376301006069759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.277 Γ— 10⁹⁸(99-digit number)
52771912079357807305…87224752602012139519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.055 Γ— 10⁹⁹(100-digit number)
10554382415871561461…74449505204024279039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.110 Γ— 10⁹⁹(100-digit number)
21108764831743122922…48899010408048558079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.221 Γ— 10⁹⁹(100-digit number)
42217529663486245844…97798020816097116159
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 956682

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 8f551cd52194e775a5b8e0628b3a2011d5c6b8b72963032be412b4a4f84f9bf4

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 #956,682 on Chainz β†—
Circulating Supply:57,860,232 XPMΒ·at block #6,827,006 Β· updates every 60s
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