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Home/Chain Registry/Block #1,780,951

Block #1,780,951

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/26/2016, 8:04:55 PM Β· Difficulty 10.7651 Β· 5,064,151 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9b28995694e4a012e2c2b7cabfd6b5b52268aa1e3f317a2c71a8a24107a5d66d
View on Chainz β†—

Difficulty

10.765082

Transactions

1

Size

199 B

Version

2

Bits

0ac3dc70

Nonce

1,263,140,389

Timestamp

9/26/2016, 8:04:55 PM

Confirmations

5,064,151

Merkle Root

29c891b7af6c83f79af03bd5564a8e0d73ed6485fbf8c48ffc01b3bf76dc252e
Transactions (1)
Coinbase29c891b7af6c83…01b3bf76dc252e
1 in β†’ 1 out8.6200 XPM109 B
AUo8UXgh…e6DYHBM3
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.

3.072 Γ— 10⁹⁡(96-digit number)
30725352661778588638…79693154175497939200
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
3.072 Γ— 10⁹⁡(96-digit number)
30725352661778588638…79693154175497939199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.145 Γ— 10⁹⁡(96-digit number)
61450705323557177276…59386308350995878399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.229 Γ— 10⁹⁢(97-digit number)
12290141064711435455…18772616701991756799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.458 Γ— 10⁹⁢(97-digit number)
24580282129422870910…37545233403983513599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.916 Γ— 10⁹⁢(97-digit number)
49160564258845741821…75090466807967027199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.832 Γ— 10⁹⁢(97-digit number)
98321128517691483642…50180933615934054399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.966 Γ— 10⁹⁷(98-digit number)
19664225703538296728…00361867231868108799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.932 Γ— 10⁹⁷(98-digit number)
39328451407076593457…00723734463736217599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.865 Γ— 10⁹⁷(98-digit number)
78656902814153186914…01447468927472435199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.573 Γ— 10⁹⁸(99-digit number)
15731380562830637382…02894937854944870399
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 1780951

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 9b28995694e4a012e2c2b7cabfd6b5b52268aa1e3f317a2c71a8a24107a5d66d

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 #1,780,951 on Chainz β†—
Circulating Supply:58,005,243 XPMΒ·at block #6,845,101 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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