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Block #280,046

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/28/2013, 1:31:26 PM Β· Difficulty 9.9735 Β· 6,531,693 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
88bf0bd0cfd7b2ca4038f2c8b30bb171fdf83e2bf46b33442a9cb94625d86e7b
View on Chainz β†—

Height

#280,046

Difficulty

9.973456

Transactions

1

Size

206 B

Version

2

Bits

09f93464

Nonce

6,230

Timestamp

11/28/2013, 1:31:26 PM

Confirmations

6,531,693

Merkle Root

35a5c5ac057757101d207db4844d183eadffae12b68c82bd788419bbd7370855
Transactions (1)
Coinbase35a5c5ac057757…8419bbd7370855
1 in β†’ 1 out10.0400 XPM116 B
AcLBm5Z9…S683d7c3
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.

3.242 Γ— 10⁹³(94-digit number)
32423149334399925316…46583360270527907940
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
3.242 Γ— 10⁹³(94-digit number)
32423149334399925316…46583360270527907939
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.484 Γ— 10⁹³(94-digit number)
64846298668799850632…93166720541055815879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.296 Γ— 10⁹⁴(95-digit number)
12969259733759970126…86333441082111631759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.593 Γ— 10⁹⁴(95-digit number)
25938519467519940253…72666882164223263519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.187 Γ— 10⁹⁴(95-digit number)
51877038935039880506…45333764328446527039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.037 Γ— 10⁹⁡(96-digit number)
10375407787007976101…90667528656893054079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.075 Γ— 10⁹⁡(96-digit number)
20750815574015952202…81335057313786108159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.150 Γ— 10⁹⁡(96-digit number)
41501631148031904405…62670114627572216319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.300 Γ— 10⁹⁡(96-digit number)
83003262296063808810…25340229255144432639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.660 Γ— 10⁹⁢(97-digit number)
16600652459212761762…50680458510288865279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.320 Γ— 10⁹⁢(97-digit number)
33201304918425523524…01360917020577730559
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 280046

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 88bf0bd0cfd7b2ca4038f2c8b30bb171fdf83e2bf46b33442a9cb94625d86e7b

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 #280,046 on Chainz β†—
Circulating Supply:57,738,021 XPMΒ·at block #6,811,738 Β· updates every 60s
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