XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,317,356

Block #1,317,356

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/7/2015, 7:01:21 PM Β· Difficulty 10.8622 Β· 5,507,436 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ee34b61138842c8f99f4dae5ae5e680de5294b031d52d27ec3b8aecba8970469
View on Chainz β†—

Difficulty

10.862156

Transactions

1

Size

243 B

Version

2

Bits

0adcb644

Nonce

74,835,731

Timestamp

11/7/2015, 7:01:21 PM

Confirmations

5,507,436

Merkle Root

cbf89f9efb53b4ea1004222d5e1e034b0708fa0a62ae4aed5830b59e2fe1d889
Transactions (1)
Coinbasecbf89f9efb53b4…30b59e2fe1d889
1 in β†’ 2 out8.4600 XPM152 B
AbNVgXWJ…g3uNfMnjALPu3s2c…EJXLjVFh
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.

5.322 Γ— 10⁹⁷(98-digit number)
53227036080346744201…31961203942830295040
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
5.322 Γ— 10⁹⁷(98-digit number)
53227036080346744201…31961203942830295039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.064 Γ— 10⁹⁸(99-digit number)
10645407216069348840…63922407885660590079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.129 Γ— 10⁹⁸(99-digit number)
21290814432138697680…27844815771321180159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.258 Γ— 10⁹⁸(99-digit number)
42581628864277395361…55689631542642360319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.516 Γ— 10⁹⁸(99-digit number)
85163257728554790722…11379263085284720639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.703 Γ— 10⁹⁹(100-digit number)
17032651545710958144…22758526170569441279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.406 Γ— 10⁹⁹(100-digit number)
34065303091421916288…45517052341138882559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.813 Γ— 10⁹⁹(100-digit number)
68130606182843832577…91034104682277765119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.362 Γ— 10¹⁰⁰(101-digit number)
13626121236568766515…82068209364555530239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.725 Γ— 10¹⁰⁰(101-digit number)
27252242473137533031…64136418729111060479
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 1317356

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 ee34b61138842c8f99f4dae5ae5e680de5294b031d52d27ec3b8aecba8970469

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 #1,317,356 on Chainz β†—
Circulating Supply:57,842,411 XPMΒ·at block #6,824,791 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