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Block #2,177,589

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/25/2017, 3:56:08 PM Β· Difficulty 10.9232 Β· 4,663,164 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ff74f633ff3922fa216a4d0c29044a55f082572ac9acec77ee93b1189d22323f
View on Chainz β†—

Difficulty

10.923158

Transactions

1

Size

201 B

Version

2

Bits

0aec5410

Nonce

792,701,309

Timestamp

6/25/2017, 3:56:08 PM

Confirmations

4,663,164

Merkle Root

2da3f37ab2cb6411794979910264453359a31612e4cadd1ce6e31e91f3695d3f
Transactions (1)
Coinbase2da3f37ab2cb64…e31e91f3695d3f
1 in β†’ 1 out8.3700 XPM110 B
AWg63fJb…QkmZCE3E
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.

1.079 Γ— 10⁹⁢(97-digit number)
10791715863217483691…51277169835243765760
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
1.079 Γ— 10⁹⁢(97-digit number)
10791715863217483691…51277169835243765759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.158 Γ— 10⁹⁢(97-digit number)
21583431726434967383…02554339670487531519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.316 Γ— 10⁹⁢(97-digit number)
43166863452869934767…05108679340975063039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.633 Γ— 10⁹⁢(97-digit number)
86333726905739869534…10217358681950126079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.726 Γ— 10⁹⁷(98-digit number)
17266745381147973906…20434717363900252159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.453 Γ— 10⁹⁷(98-digit number)
34533490762295947813…40869434727800504319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.906 Γ— 10⁹⁷(98-digit number)
69066981524591895627…81738869455601008639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.381 Γ— 10⁹⁸(99-digit number)
13813396304918379125…63477738911202017279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.762 Γ— 10⁹⁸(99-digit number)
27626792609836758251…26955477822404034559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.525 Γ— 10⁹⁸(99-digit number)
55253585219673516502…53910955644808069119
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 2177589

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 ff74f633ff3922fa216a4d0c29044a55f082572ac9acec77ee93b1189d22323f

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 #2,177,589 on Chainz β†—
Circulating Supply:57,970,366 XPMΒ·at block #6,840,752 Β· updates every 60s
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