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Block #381,595

2CCLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Cunningham Chain of the Second Kind Ā· Discovered 1/30/2014, 3:12:36 AM Ā· Difficulty 10.4026 Ā· 6,419,049 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
694f264182fc06b232d5e235cbba2df4835f9d050b0164e789abe33a735673bd
View on Chainz ā†—

Height

#381,595

Difficulty

10.402644

Transactions

3

Size

807 B

Version

2

Bits

0a6713a9

Nonce

16,778,859

Timestamp

1/30/2014, 3:12:36 AM

Confirmations

6,419,049

Merkle Root

0b31ab0055e57cd515df1ce05777f8fafcf49d4b80e3337afaa65d1182901605
Transactions (3)
Coinbase5bcf19cad51bcfā€¦06339a7df0a4c3
1 in ā†’ 1 out9.2500 XPM116 B
AbwWkWZtā€¦kawDhufa
82f4391f885eb0ā€¦e9da357679225d
2 in ā†’ 2 out11.2947 XPM376 B
AbbyRCzDā€¦did3ghetATZUp49Dā€¦xaoNMsmK
5e3b5e2e38e093ā€¦7872bb5a709b7a
1 in ā†’ 2 out3.1089 XPM225 B
APVNDGajā€¦mMpeHnBjATcNZPM3ā€¦W9kVPzXy
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) ā€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.714 Ɨ 10ā¹āµ(96-digit number)
37145552491601233952ā€¦09930710741031108320
Discovered Prime Numbers
p_k = 2^k Ɨ origin + 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 + 1
3.714 Ɨ 10ā¹āµ(96-digit number)
37145552491601233952ā€¦09930710741031108321
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2āˆ’1 ā†’
2
2^1 Ɨ origin + 1
7.429 Ɨ 10ā¹āµ(96-digit number)
74291104983202467904ā€¦19861421482062216641
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2āˆ’1 ā†’
3
2^2 Ɨ origin + 1
1.485 Ɨ 10ā¹ā¶(97-digit number)
14858220996640493580ā€¦39722842964124433281
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2āˆ’1 ā†’
4
2^3 Ɨ origin + 1
2.971 Ɨ 10ā¹ā¶(97-digit number)
29716441993280987161ā€¦79445685928248866561
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2āˆ’1 ā†’
5
2^4 Ɨ origin + 1
5.943 Ɨ 10ā¹ā¶(97-digit number)
59432883986561974323ā€¦58891371856497733121
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2āˆ’1 ā†’
6
2^5 Ɨ origin + 1
1.188 Ɨ 10ā¹ā·(98-digit number)
11886576797312394864ā€¦17782743712995466241
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2āˆ’1 ā†’
7
2^6 Ɨ origin + 1
2.377 Ɨ 10ā¹ā·(98-digit number)
23773153594624789729ā€¦35565487425990932481
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2āˆ’1 ā†’
8
2^7 Ɨ origin + 1
4.754 Ɨ 10ā¹ā·(98-digit number)
47546307189249579458ā€¦71130974851981864961
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2āˆ’1 ā†’
9
2^8 Ɨ origin + 1
9.509 Ɨ 10ā¹ā·(98-digit number)
95092614378499158917ā€¦42261949703963729921
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2āˆ’1 ā†’
10
2^9 Ɨ origin + 1
1.901 Ɨ 10ā¹āø(99-digit number)
19018522875699831783ā€¦84523899407927459841
Verify on FactorDB ā†—Wolfram Alpha ā†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin ā€” the large number shown above ā€” 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 ā†’
ā˜…ā˜…ā˜†ā˜†ā˜†
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 Ɨ 3 Ɨ 5 Ɨ 7 Ɨ ā€¦), the result is the first prime in the chain. The origin is deliberately divisible by this primorial ā€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Ɨ Primorial (2Ā·3Ā·5Ā·7Ā·11Ā·ā€¦)
Source: Primecoin prime.cpp ā€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors ā€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: pā‚ (first prime), pā‚‚ = 2pā‚ āˆ’ 1, pā‚ƒ = 2pā‚‚ āˆ’ 1, ā€¦
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 381595

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 694f264182fc06b232d5e235cbba2df4835f9d050b0164e789abe33a735673bd

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 ā†’ Debug Window ā†’ 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 #381,595 on Chainz ā†—
Circulating Supply:57,649,219 XPMĀ·at block #6,800,643 Ā· updates every 60s
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