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Home/Chain Registry/Block #175,916

Block #175,916

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/22/2013, 2:56:10 PM Β· Difficulty 9.8643 Β· 6,650,336 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
260b5ecc92c2fcc76d32203b0d6ba125e005533b75ae0fa511f69c18986bc243
View on Chainz β†—

Height

#175,916

Difficulty

9.864326

Transactions

1

Size

200 B

Version

2

Bits

09dd4480

Nonce

128,606

Timestamp

9/22/2013, 2:56:10 PM

Confirmations

6,650,336

Merkle Root

a9e0cd2e12c1edafc1ffc2f1bd89b21e89c73deaff5a8c9a420485dc54f99ade
Transactions (1)
Coinbasea9e0cd2e12c1ed…0485dc54f99ade
1 in β†’ 1 out10.2600 XPM110 B
AYPWofJe…9BpDnsXh
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.

6.996 Γ— 10⁹³(94-digit number)
69962620302703436709…51507950183629853240
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
6.996 Γ— 10⁹³(94-digit number)
69962620302703436709…51507950183629853239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.399 Γ— 10⁹⁴(95-digit number)
13992524060540687341…03015900367259706479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.798 Γ— 10⁹⁴(95-digit number)
27985048121081374683…06031800734519412959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.597 Γ— 10⁹⁴(95-digit number)
55970096242162749367…12063601469038825919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.119 Γ— 10⁹⁡(96-digit number)
11194019248432549873…24127202938077651839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.238 Γ— 10⁹⁡(96-digit number)
22388038496865099747…48254405876155303679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.477 Γ— 10⁹⁡(96-digit number)
44776076993730199494…96508811752310607359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.955 Γ— 10⁹⁡(96-digit number)
89552153987460398988…93017623504621214719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.791 Γ— 10⁹⁢(97-digit number)
17910430797492079797…86035247009242429439
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 175916

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 260b5ecc92c2fcc76d32203b0d6ba125e005533b75ae0fa511f69c18986bc243

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 #175,916 on Chainz β†—
Circulating Supply:57,854,149 XPMΒ·at block #6,826,251 Β· updates every 60s
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