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Home/Chain Registry/Block #2,177,349

Block #2,177,349

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/25/2017, 12:38:34 PM Β· Difficulty 10.9225 Β· 4,662,702 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ab3e9fabfbe9009c101f84b409a5abc2c8a860439efc6a2a82644cd8aed059c4
View on Chainz β†—

Difficulty

10.922510

Transactions

1

Size

199 B

Version

2

Bits

0aec29a0

Nonce

314,590,872

Timestamp

6/25/2017, 12:38:34 PM

Confirmations

4,662,702

Merkle Root

372b81e9cba4bdab50f05a14f4efe3c47320a2fdd9a8b40e32b66f5cb96c5ab4
Transactions (1)
Coinbase372b81e9cba4bd…b66f5cb96c5ab4
1 in β†’ 1 out8.3700 XPM110 B
AbgzJfVe…WRqrMZnW
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.

2.195 Γ— 10⁹²(93-digit number)
21951043968225064951…24126183038500326240
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
2.195 Γ— 10⁹²(93-digit number)
21951043968225064951…24126183038500326239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.390 Γ— 10⁹²(93-digit number)
43902087936450129903…48252366077000652479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.780 Γ— 10⁹²(93-digit number)
87804175872900259806…96504732154001304959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.756 Γ— 10⁹³(94-digit number)
17560835174580051961…93009464308002609919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.512 Γ— 10⁹³(94-digit number)
35121670349160103922…86018928616005219839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.024 Γ— 10⁹³(94-digit number)
70243340698320207845…72037857232010439679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.404 Γ— 10⁹⁴(95-digit number)
14048668139664041569…44075714464020879359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.809 Γ— 10⁹⁴(95-digit number)
28097336279328083138…88151428928041758719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.619 Γ— 10⁹⁴(95-digit number)
56194672558656166276…76302857856083517439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.123 Γ— 10⁹⁡(96-digit number)
11238934511731233255…52605715712167034879
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 2177349

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 ab3e9fabfbe9009c101f84b409a5abc2c8a860439efc6a2a82644cd8aed059c4

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 #2,177,349 on Chainz β†—
Circulating Supply:57,964,717 XPMΒ·at block #6,840,050 Β· updates every 60s
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