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Block #201,883

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/9/2013, 9:35:57 PM Β· Difficulty 9.8935 Β· 6,598,532 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e4f0653dea1a479c659afc8bb9f97bffdf1fdd66890844b55dedbce428828ff9
View on Chainz β†—

Height

#201,883

Difficulty

9.893527

Transactions

1

Size

207 B

Version

2

Bits

09e4be33

Nonce

1,361,126

Timestamp

10/9/2013, 9:35:57 PM

Confirmations

6,598,532

Merkle Root

eb8f4ab20066a5b364540314ef3fa271785c17edb17b2048a69d9c4846b21ae2
Transactions (1)
Coinbaseeb8f4ab20066a5…9d9c4846b21ae2
1 in β†’ 1 out10.2000 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.

2.142 Γ— 10⁹⁷(98-digit number)
21427101693781230412…17249523057657869240
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
2.142 Γ— 10⁹⁷(98-digit number)
21427101693781230412…17249523057657869239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.285 Γ— 10⁹⁷(98-digit number)
42854203387562460825…34499046115315738479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.570 Γ— 10⁹⁷(98-digit number)
85708406775124921650…68998092230631476959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.714 Γ— 10⁹⁸(99-digit number)
17141681355024984330…37996184461262953919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.428 Γ— 10⁹⁸(99-digit number)
34283362710049968660…75992368922525907839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.856 Γ— 10⁹⁸(99-digit number)
68566725420099937320…51984737845051815679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.371 Γ— 10⁹⁹(100-digit number)
13713345084019987464…03969475690103631359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.742 Γ— 10⁹⁹(100-digit number)
27426690168039974928…07938951380207262719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.485 Γ— 10⁹⁹(100-digit number)
54853380336079949856…15877902760414525439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.097 Γ— 10¹⁰⁰(101-digit number)
10970676067215989971…31755805520829050879
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 201883

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 e4f0653dea1a479c659afc8bb9f97bffdf1fdd66890844b55dedbce428828ff9

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 #201,883 on Chainz β†—
Circulating Supply:57,647,385 XPMΒ·at block #6,800,414 Β· updates every 60s
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