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Home/Chain Registry/Block #202,966

Block #202,966

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/10/2013, 1:44:12 PM Β· Difficulty 9.8960 Β· 6,597,720 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b4b2fc66e26e4c6adf6cddf8ea9b19bf9a238518d9145a03ef539e071d8ab4c8
View on Chainz β†—

Height

#202,966

Difficulty

9.896029

Transactions

2

Size

424 B

Version

2

Bits

09e5622b

Nonce

514,866

Timestamp

10/10/2013, 1:44:12 PM

Confirmations

6,597,720

Merkle Root

f2e8bfcc9d66f6bb95ee561b127f34d7379ce9fc6bb9e824e0eb4cf8f7542c99
Transactions (2)
Coinbase5a715e4867d678…263b31a21cd981
1 in β†’ 1 out10.2100 XPM109 B
AU7esMd3…ab7PpnKw
c7a2daafee5e61…25805a0cd868c9
1 in β†’ 2 out2.6939 XPM226 B
ARXPuc6U…amuQkbndAbNXXQ3F…e7jXejV9
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.

1.422 Γ— 10⁹²(93-digit number)
14227075099584743960…90117784037647628900
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
1.422 Γ— 10⁹²(93-digit number)
14227075099584743960…90117784037647628899
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.845 Γ— 10⁹²(93-digit number)
28454150199169487921…80235568075295257799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.690 Γ— 10⁹²(93-digit number)
56908300398338975843…60471136150590515599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.138 Γ— 10⁹³(94-digit number)
11381660079667795168…20942272301181031199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.276 Γ— 10⁹³(94-digit number)
22763320159335590337…41884544602362062399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.552 Γ— 10⁹³(94-digit number)
45526640318671180674…83769089204724124799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.105 Γ— 10⁹³(94-digit number)
91053280637342361349…67538178409448249599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.821 Γ— 10⁹⁴(95-digit number)
18210656127468472269…35076356818896499199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.642 Γ— 10⁹⁴(95-digit number)
36421312254936944539…70152713637792998399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 202966

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 b4b2fc66e26e4c6adf6cddf8ea9b19bf9a238518d9145a03ef539e071d8ab4c8

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 #202,966 on Chainz β†—
Circulating Supply:57,649,554 XPMΒ·at block #6,800,685 Β· updates every 60s
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