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Home/Chain Registry/Block #1,714,257

Block #1,714,257

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/12/2016, 7:59:18 PM Β· Difficulty 10.6556 Β· 5,119,112 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0c2f6c6974eb11b7c620de629990cb9c3c08cb4d93ca99328db742b1740cf60d
View on Chainz β†—

Difficulty

10.655607

Transactions

1

Size

201 B

Version

2

Bits

0aa7d5e1

Nonce

668,821,771

Timestamp

8/12/2016, 7:59:18 PM

Confirmations

5,119,112

Merkle Root

af73ba7e5dee2d62559d7099e6a3d2a462b916c2f2ec393d296053d7b1ff6203
Transactions (1)
Coinbaseaf73ba7e5dee2d…6053d7b1ff6203
1 in β†’ 1 out8.7900 XPM110 B
AJWnR1aj…9q93J5q9
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.

6.801 Γ— 10⁹⁢(97-digit number)
68016351444053285960…92540202753601464320
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
6.801 Γ— 10⁹⁢(97-digit number)
68016351444053285960…92540202753601464319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.360 Γ— 10⁹⁷(98-digit number)
13603270288810657192…85080405507202928639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.720 Γ— 10⁹⁷(98-digit number)
27206540577621314384…70160811014405857279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.441 Γ— 10⁹⁷(98-digit number)
54413081155242628768…40321622028811714559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.088 Γ— 10⁹⁸(99-digit number)
10882616231048525753…80643244057623429119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.176 Γ— 10⁹⁸(99-digit number)
21765232462097051507…61286488115246858239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.353 Γ— 10⁹⁸(99-digit number)
43530464924194103014…22572976230493716479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.706 Γ— 10⁹⁸(99-digit number)
87060929848388206029…45145952460987432959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.741 Γ— 10⁹⁹(100-digit number)
17412185969677641205…90291904921974865919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.482 Γ— 10⁹⁹(100-digit number)
34824371939355282411…80583809843949731839
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 1714257

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 0c2f6c6974eb11b7c620de629990cb9c3c08cb4d93ca99328db742b1740cf60d

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 #1,714,257 on Chainz β†—
Circulating Supply:57,911,149 XPMΒ·at block #6,833,368 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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