XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #208,214

Block #208,214

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/13/2013, 9:31:18 PM Β· Difficulty 9.9054 Β· 6,618,701 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1dc064bdebb70c9419c8d419191f6a67b39d4da09cf78d28cb865b622c45e5f0
View on Chainz β†—

Height

#208,214

Difficulty

9.905357

Transactions

2

Size

508 B

Version

2

Bits

09e7c582

Nonce

20,625

Timestamp

10/13/2013, 9:31:18 PM

Confirmations

6,618,701

Merkle Root

61e4cb024f75173f0629989aa907a1a322888020c8cf950c0e6526e2d34ac1c6
Transactions (2)
Coinbase0d043c12df294c…0d0a0165cd0fef
1 in β†’ 1 out10.1900 XPM109 B
AQmhVit2…9HPyJpi9
2cf8b1e84193a2…ce1af9b323bae1
2 in β†’ 2 out20.5400 XPM308 B
Aa4s3Z6Y…Pg1PYaikANsvDN5K…jwzDHo7V
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.

6.253 Γ— 10⁹⁢(97-digit number)
62537896729212470303…01960295827627591680
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
6.253 Γ— 10⁹⁢(97-digit number)
62537896729212470303…01960295827627591679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.250 Γ— 10⁹⁷(98-digit number)
12507579345842494060…03920591655255183359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.501 Γ— 10⁹⁷(98-digit number)
25015158691684988121…07841183310510366719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.003 Γ— 10⁹⁷(98-digit number)
50030317383369976243…15682366621020733439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.000 Γ— 10⁹⁸(99-digit number)
10006063476673995248…31364733242041466879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.001 Γ— 10⁹⁸(99-digit number)
20012126953347990497…62729466484082933759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.002 Γ— 10⁹⁸(99-digit number)
40024253906695980994…25458932968165867519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.004 Γ— 10⁹⁸(99-digit number)
80048507813391961988…50917865936331735039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.600 Γ— 10⁹⁹(100-digit number)
16009701562678392397…01835731872663470079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 208214

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 1dc064bdebb70c9419c8d419191f6a67b39d4da09cf78d28cb865b622c45e5f0

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 #208,214 on Chainz β†—
Circulating Supply:57,859,489 XPMΒ·at block #6,826,914 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