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Block #267,221

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/21/2013, 2:49:03 AM Β· Difficulty 9.9593 Β· 6,528,540 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d19bd6894471b50e6bd9b5bb1091f7f769cd724b3ae76face85ab4da4e0888c2
View on Chainz β†—

Height

#267,221

Difficulty

9.959292

Transactions

2

Size

427 B

Version

2

Bits

09f59430

Nonce

80,531

Timestamp

11/21/2013, 2:49:03 AM

Confirmations

6,528,540

Merkle Root

c8ff5ddf9baecf4807e861bdbd7aaa4a43ed3fab5fd35f379c33e59c17f54037
Transactions (2)
Coinbasec6c412406f71e7…655d9b540bf435
1 in β†’ 1 out10.0800 XPM110 B
AeKNrjNj…1NEq95Ta
37d6f8d575c579…383f8f1c8f3e67
1 in β†’ 2 out3.3655 XPM226 B
ARC3GLtb…BSXvSmKgAeKNrjNj…1NEq95Ta
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.

1.088 Γ— 10⁹⁷(98-digit number)
10883285767395428435…36039861175939658240
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
1.088 Γ— 10⁹⁷(98-digit number)
10883285767395428435…36039861175939658239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.176 Γ— 10⁹⁷(98-digit number)
21766571534790856870…72079722351879316479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.353 Γ— 10⁹⁷(98-digit number)
43533143069581713740…44159444703758632959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.706 Γ— 10⁹⁷(98-digit number)
87066286139163427481…88318889407517265919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.741 Γ— 10⁹⁸(99-digit number)
17413257227832685496…76637778815034531839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.482 Γ— 10⁹⁸(99-digit number)
34826514455665370992…53275557630069063679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.965 Γ— 10⁹⁸(99-digit number)
69653028911330741985…06551115260138127359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.393 Γ— 10⁹⁹(100-digit number)
13930605782266148397…13102230520276254719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.786 Γ— 10⁹⁹(100-digit number)
27861211564532296794…26204461040552509439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.572 Γ— 10⁹⁹(100-digit number)
55722423129064593588…52408922081105018879
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 267221

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 d19bd6894471b50e6bd9b5bb1091f7f769cd724b3ae76face85ab4da4e0888c2

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 #267,221 on Chainz β†—
Circulating Supply:57,610,169 XPMΒ·at block #6,795,760 Β· updates every 60s
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