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Home/Chain Registry/Block #965,086

Block #965,086

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/7/2015, 11:11:27 PM Β· Difficulty 10.8585 Β· 5,879,630 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7a0864af71e1877ec080a9644fae565f150b31b09b6a2ebfcc3d7d5447762f0b
View on Chainz β†—

Height

#965,086

Difficulty

10.858530

Transactions

1

Size

199 B

Version

2

Bits

0adbc899

Nonce

2,030,683,889

Timestamp

3/7/2015, 11:11:27 PM

Confirmations

5,879,630

Merkle Root

1e212ad16ac84768603d14e87e121bb4f0d212ade515e39b1b93c5f35d08864b
Transactions (1)
Coinbase1e212ad16ac847…93c5f35d08864b
1 in β†’ 1 out8.4700 XPM110 B
ANqeSCwe…9kCb2xwz
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.

3.878 Γ— 10⁹¹(92-digit number)
38784585121212871313…01739606343760318920
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
3.878 Γ— 10⁹¹(92-digit number)
38784585121212871313…01739606343760318919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.756 Γ— 10⁹¹(92-digit number)
77569170242425742627…03479212687520637839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.551 Γ— 10⁹²(93-digit number)
15513834048485148525…06958425375041275679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.102 Γ— 10⁹²(93-digit number)
31027668096970297051…13916850750082551359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.205 Γ— 10⁹²(93-digit number)
62055336193940594102…27833701500165102719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.241 Γ— 10⁹³(94-digit number)
12411067238788118820…55667403000330205439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.482 Γ— 10⁹³(94-digit number)
24822134477576237640…11334806000660410879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.964 Γ— 10⁹³(94-digit number)
49644268955152475281…22669612001320821759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.928 Γ— 10⁹³(94-digit number)
99288537910304950563…45339224002641643519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.985 Γ— 10⁹⁴(95-digit number)
19857707582060990112…90678448005283287039
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 965086

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 7a0864af71e1877ec080a9644fae565f150b31b09b6a2ebfcc3d7d5447762f0b

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 #965,086 on Chainz β†—
Circulating Supply:58,002,137 XPMΒ·at block #6,844,715 Β· updates every 60s
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