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Block #964,395

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/7/2015, 12:23:38 AM Β· Difficulty 10.8763 Β· 5,860,298 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d46ab716f9991f4a2fb95e6badecf9dc43b7908983e08cb290c3aa16b0a3f663
View on Chainz β†—

Height

#964,395

Difficulty

10.876258

Transactions

1

Size

207 B

Version

2

Bits

0ae05277

Nonce

427,117,353

Timestamp

3/7/2015, 12:23:38 AM

Confirmations

5,860,298

Merkle Root

b0b47512ff295a8fbe9060f6ca333363c3123af87794199985353e7dd5541fc7
Transactions (1)
Coinbaseb0b47512ff295a…353e7dd5541fc7
1 in β†’ 1 out8.4400 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.613 Γ— 10⁹⁷(98-digit number)
16136863365725138261…18666050334398956160
Discovered Prime Numbers
p_k = 2^k Γ— 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
1.613 Γ— 10⁹⁷(98-digit number)
16136863365725138261…18666050334398956161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.227 Γ— 10⁹⁷(98-digit number)
32273726731450276523…37332100668797912321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.454 Γ— 10⁹⁷(98-digit number)
64547453462900553047…74664201337595824641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.290 Γ— 10⁹⁸(99-digit number)
12909490692580110609…49328402675191649281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.581 Γ— 10⁹⁸(99-digit number)
25818981385160221219…98656805350383298561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.163 Γ— 10⁹⁸(99-digit number)
51637962770320442438…97313610700766597121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.032 Γ— 10⁹⁹(100-digit number)
10327592554064088487…94627221401533194241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.065 Γ— 10⁹⁹(100-digit number)
20655185108128176975…89254442803066388481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.131 Γ— 10⁹⁹(100-digit number)
41310370216256353950…78508885606132776961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.262 Γ— 10⁹⁹(100-digit number)
82620740432512707901…57017771212265553921
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 964395

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 d46ab716f9991f4a2fb95e6badecf9dc43b7908983e08cb290c3aa16b0a3f663

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 #964,395 on Chainz β†—
Circulating Supply:57,841,611 XPMΒ·at block #6,824,692 Β· updates every 60s
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