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Home/Chain Registry/Block #2,551,381

Block #2,551,381

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/6/2018, 6:00:02 AM Β· Difficulty 10.9893 Β· 4,280,474 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ea0d1a4bace447aa761a774afe54ebb409d745c6844e519fd7eed29a65b05547
View on Chainz β†—

Difficulty

10.989340

Transactions

1

Size

200 B

Version

2

Bits

0afd4569

Nonce

830,567,790

Timestamp

3/6/2018, 6:00:02 AM

Confirmations

4,280,474

Merkle Root

ade21322853144ce8073856560d2652b8c5856d1b1ba7262410bdc6b9cbbe47d
Transactions (1)
Coinbaseade21322853144…0bdc6b9cbbe47d
1 in β†’ 1 out8.2700 XPM110 B
AURjybpg…KHKMxjfS
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.

1.285 Γ— 10⁹⁴(95-digit number)
12855328729271429985…47617825441113171200
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
1.285 Γ— 10⁹⁴(95-digit number)
12855328729271429985…47617825441113171199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.571 Γ— 10⁹⁴(95-digit number)
25710657458542859971…95235650882226342399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.142 Γ— 10⁹⁴(95-digit number)
51421314917085719942…90471301764452684799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.028 Γ— 10⁹⁡(96-digit number)
10284262983417143988…80942603528905369599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.056 Γ— 10⁹⁡(96-digit number)
20568525966834287977…61885207057810739199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.113 Γ— 10⁹⁡(96-digit number)
41137051933668575954…23770414115621478399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.227 Γ— 10⁹⁡(96-digit number)
82274103867337151908…47540828231242956799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.645 Γ— 10⁹⁢(97-digit number)
16454820773467430381…95081656462485913599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.290 Γ— 10⁹⁢(97-digit number)
32909641546934860763…90163312924971827199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.581 Γ— 10⁹⁢(97-digit number)
65819283093869721526…80326625849943654399
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 2551381

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 ea0d1a4bace447aa761a774afe54ebb409d745c6844e519fd7eed29a65b05547

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 #2,551,381 on Chainz β†—
Circulating Supply:57,898,961 XPMΒ·at block #6,831,854 Β· updates every 60s
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