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Block #174,757

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/21/2013, 9:08:43 PM Β· Difficulty 9.8618 Β· 6,625,880 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
76c8d9c9abd21b07dffdc2fa597fcb32c992043e6e8c8cc3426113cdd25a7779
View on Chainz β†—

Height

#174,757

Difficulty

9.861825

Transactions

1

Size

203 B

Version

2

Bits

09dca094

Nonce

1,051

Timestamp

9/21/2013, 9:08:43 PM

Confirmations

6,625,880

Merkle Root

3cc5ecc0b301e57013f7ab0d1173d9b3f3387feada9922326d09f897bc7fca8b
Transactions (1)
Coinbase3cc5ecc0b301e5…09f897bc7fca8b
1 in β†’ 1 out10.2700 XPM112 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.

3.516 Γ— 10⁹⁢(97-digit number)
35163662721532642591…91892629688371905920
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
3.516 Γ— 10⁹⁢(97-digit number)
35163662721532642591…91892629688371905919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.032 Γ— 10⁹⁢(97-digit number)
70327325443065285182…83785259376743811839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.406 Γ— 10⁹⁷(98-digit number)
14065465088613057036…67570518753487623679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.813 Γ— 10⁹⁷(98-digit number)
28130930177226114073…35141037506975247359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.626 Γ— 10⁹⁷(98-digit number)
56261860354452228146…70282075013950494719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.125 Γ— 10⁹⁸(99-digit number)
11252372070890445629…40564150027900989439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.250 Γ— 10⁹⁸(99-digit number)
22504744141780891258…81128300055801978879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.500 Γ— 10⁹⁸(99-digit number)
45009488283561782516…62256600111603957759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.001 Γ— 10⁹⁸(99-digit number)
90018976567123565033…24513200223207915519
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 174757

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 76c8d9c9abd21b07dffdc2fa597fcb32c992043e6e8c8cc3426113cdd25a7779

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 #174,757 on Chainz β†—
Circulating Supply:57,649,161 XPMΒ·at block #6,800,636 Β· updates every 60s
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