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Home/Chain Registry/Block #787,754

Block #787,754

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/29/2014, 7:13:03 AM Β· Difficulty 10.9745 Β· 6,057,322 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0fb956fa8984a5b6ae86aacfe87a14f71e986ec930aa9627a05574c493ed8870
View on Chainz β†—

Height

#787,754

Difficulty

10.974522

Transactions

1

Size

206 B

Version

2

Bits

0af97a43

Nonce

1,870,508,613

Timestamp

10/29/2014, 7:13:03 AM

Confirmations

6,057,322

Merkle Root

70841919e20ea8c1ea8eca6db318d31230de8ac5144307ebc59f9c76043818ac
Transactions (1)
Coinbase70841919e20ea8…9f9c76043818ac
1 in β†’ 1 out8.2900 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.

3.430 Γ— 10⁹⁡(96-digit number)
34303185850903116236…03748414208315330560
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
3.430 Γ— 10⁹⁡(96-digit number)
34303185850903116236…03748414208315330559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.860 Γ— 10⁹⁡(96-digit number)
68606371701806232473…07496828416630661119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.372 Γ— 10⁹⁢(97-digit number)
13721274340361246494…14993656833261322239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.744 Γ— 10⁹⁢(97-digit number)
27442548680722492989…29987313666522644479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.488 Γ— 10⁹⁢(97-digit number)
54885097361444985978…59974627333045288959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.097 Γ— 10⁹⁷(98-digit number)
10977019472288997195…19949254666090577919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.195 Γ— 10⁹⁷(98-digit number)
21954038944577994391…39898509332181155839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.390 Γ— 10⁹⁷(98-digit number)
43908077889155988783…79797018664362311679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.781 Γ— 10⁹⁷(98-digit number)
87816155778311977566…59594037328724623359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.756 Γ— 10⁹⁸(99-digit number)
17563231155662395513…19188074657449246719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.512 Γ— 10⁹⁸(99-digit number)
35126462311324791026…38376149314898493439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 787754

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 0fb956fa8984a5b6ae86aacfe87a14f71e986ec930aa9627a05574c493ed8870

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 #787,754 on Chainz β†—
Circulating Supply:58,005,034 XPMΒ·at block #6,845,075 Β· updates every 60s
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