XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,681,603

Block #1,681,603

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2016, 11:07:37 AM Β· Difficulty 10.7163 Β· 5,149,946 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
697d6c3dda0d18ca8e21bf5a894db9db74ad9c4159af1e956dd6aabe4e9fee92
View on Chainz β†—

Difficulty

10.716263

Transactions

2

Size

573 B

Version

2

Bits

0ab75cff

Nonce

65,302,763

Timestamp

7/20/2016, 11:07:37 AM

Confirmations

5,149,946

Merkle Root

dfdac098ab8b6e0d0ff5443fa09c8e560ffba27ec8fbd6e6862d8430543e8313
Transactions (2)
Coinbase46d288b6b863c4…9481feef3ea09c
1 in β†’ 1 out8.7000 XPM110 B
AGsfZFob…JfPEapyM
4ea5cd9b273a76…d41f2c0c14f1a3
2 in β†’ 2 out0.6379 XPM373 B
AKNRrvw2…AF8oSenfAdPbYFiv…u96avMWk
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.

1.572 Γ— 10⁹⁡(96-digit number)
15723914617857094374…34745638352480888640
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.572 Γ— 10⁹⁡(96-digit number)
15723914617857094374…34745638352480888641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.144 Γ— 10⁹⁡(96-digit number)
31447829235714188749…69491276704961777281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.289 Γ— 10⁹⁡(96-digit number)
62895658471428377499…38982553409923554561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.257 Γ— 10⁹⁢(97-digit number)
12579131694285675499…77965106819847109121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.515 Γ— 10⁹⁢(97-digit number)
25158263388571350999…55930213639694218241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.031 Γ— 10⁹⁢(97-digit number)
50316526777142701999…11860427279388436481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.006 Γ— 10⁹⁷(98-digit number)
10063305355428540399…23720854558776872961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.012 Γ— 10⁹⁷(98-digit number)
20126610710857080799…47441709117553745921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.025 Γ— 10⁹⁷(98-digit number)
40253221421714161599…94883418235107491841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.050 Γ— 10⁹⁷(98-digit number)
80506442843428323198…89766836470214983681
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 1681603

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 697d6c3dda0d18ca8e21bf5a894db9db74ad9c4159af1e956dd6aabe4e9fee92

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 #1,681,603 on Chainz β†—
Circulating Supply:57,896,483 XPMΒ·at block #6,831,548 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy