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Home/Chain Registry/Block #1,704,658

Block #1,704,658

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/6/2016, 2:08:55 AM Β· Difficulty 10.6627 Β· 5,120,200 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fd52dbc819cac6f0e97ab3b1499b8ab3a8152dec7d8fe1f74daa77d52c339152
View on Chainz β†—

Difficulty

10.662665

Transactions

1

Size

201 B

Version

2

Bits

0aa9a46f

Nonce

704,047,265

Timestamp

8/6/2016, 2:08:55 AM

Confirmations

5,120,200

Merkle Root

7c0c961f40e2f9f110239b5668a3beb4d4382b265de6d5d709cc0c3d9a666fd7
Transactions (1)
Coinbase7c0c961f40e2f9…cc0c3d9a666fd7
1 in β†’ 1 out8.7800 XPM110 B
AWfefSWf…n2YvPELa
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.

1.367 Γ— 10⁹⁢(97-digit number)
13670439201814327611…31309225450954625280
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
1.367 Γ— 10⁹⁢(97-digit number)
13670439201814327611…31309225450954625279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.734 Γ— 10⁹⁢(97-digit number)
27340878403628655222…62618450901909250559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.468 Γ— 10⁹⁢(97-digit number)
54681756807257310444…25236901803818501119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.093 Γ— 10⁹⁷(98-digit number)
10936351361451462088…50473803607637002239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.187 Γ— 10⁹⁷(98-digit number)
21872702722902924177…00947607215274004479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.374 Γ— 10⁹⁷(98-digit number)
43745405445805848355…01895214430548008959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.749 Γ— 10⁹⁷(98-digit number)
87490810891611696710…03790428861096017919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.749 Γ— 10⁹⁸(99-digit number)
17498162178322339342…07580857722192035839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.499 Γ— 10⁹⁸(99-digit number)
34996324356644678684…15161715444384071679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.999 Γ— 10⁹⁸(99-digit number)
69992648713289357368…30323430888768143359
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 1704658

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 fd52dbc819cac6f0e97ab3b1499b8ab3a8152dec7d8fe1f74daa77d52c339152

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 #1,704,658 on Chainz β†—
Circulating Supply:57,842,947 XPMΒ·at block #6,824,857 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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