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Home/Chain Registry/Block #2,177,495

Block #2,177,495

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/25/2017, 2:32:21 PM Β· Difficulty 10.9230 Β· 4,663,254 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9ae0eefb792af42c3b367f3d184f56b9001dd0817c1d893d73f89dd3c48e7e14
View on Chainz β†—

Difficulty

10.922999

Transactions

1

Size

200 B

Version

2

Bits

0aec49aa

Nonce

2,034,658,636

Timestamp

6/25/2017, 2:32:21 PM

Confirmations

4,663,254

Merkle Root

02bdcffcdba642f6b62a8ea4f6a2845259c3fb84ac4122d6e565cfcfc80b9439
Transactions (1)
Coinbase02bdcffcdba642…65cfcfc80b9439
1 in β†’ 1 out8.3700 XPM110 B
AScEvZx4…tQM4mGiy
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.

1.324 Γ— 10⁹⁴(95-digit number)
13242893234132446269…88481169294349189120
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
1.324 Γ— 10⁹⁴(95-digit number)
13242893234132446269…88481169294349189119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.648 Γ— 10⁹⁴(95-digit number)
26485786468264892538…76962338588698378239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.297 Γ— 10⁹⁴(95-digit number)
52971572936529785076…53924677177396756479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.059 Γ— 10⁹⁡(96-digit number)
10594314587305957015…07849354354793512959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.118 Γ— 10⁹⁡(96-digit number)
21188629174611914030…15698708709587025919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.237 Γ— 10⁹⁡(96-digit number)
42377258349223828061…31397417419174051839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.475 Γ— 10⁹⁡(96-digit number)
84754516698447656123…62794834838348103679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.695 Γ— 10⁹⁢(97-digit number)
16950903339689531224…25589669676696207359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.390 Γ— 10⁹⁢(97-digit number)
33901806679379062449…51179339353392414719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.780 Γ— 10⁹⁢(97-digit number)
67803613358758124898…02358678706784829439
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 2177495

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 9ae0eefb792af42c3b367f3d184f56b9001dd0817c1d893d73f89dd3c48e7e14

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 #2,177,495 on Chainz β†—
Circulating Supply:57,970,335 XPMΒ·at block #6,840,748 Β· updates every 60s
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