XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #163,468

Block #163,468

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2013, 12:28:51 AM Β· Difficulty 9.8620 Β· 6,637,135 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d7b5af39542c600c55e2bf67246f162772b0d7fe2e7938e3bb74aadfffc5e29f
View on Chainz β†—

Height

#163,468

Difficulty

9.861967

Transactions

5

Size

1.03 KB

Version

2

Bits

09dca9e4

Nonce

11,339

Timestamp

9/14/2013, 12:28:51 AM

Confirmations

6,637,135

Merkle Root

7a2fd4b7fef0a062824474a40c1bf122555080552d0736a8bee0e453fcc23c4e
Transactions (5)
Coinbase47ea91c309b768…716e4ab17e89f3
1 in β†’ 1 out10.3100 XPM109 B
AcCkGn5P…AV5Z1v4o
c95634090a7aba…2057f1369bcd7b
2 in β†’ 1 out20.5300 XPM270 B
AH9D5N1B…4NXoLsWQ
d7ce8eb7615342…3c2c1eb57fb592
2 in β†’ 1 out20.5200 XPM274 B
AH9D5N1B…4NXoLsWQ
0b7abd8dc6734b…fa321171cef6f0
1 in β†’ 1 out10.2600 XPM158 B
AH9D5N1B…4NXoLsWQ
e3f7c21bf7d9e6…e9fe7c33c11b91
1 in β†’ 1 out10.2600 XPM158 B
AH9D5N1B…4NXoLsWQ
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.

1.404 Γ— 10⁹¹(92-digit number)
14041620712678021134…58768085376982596640
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
1.404 Γ— 10⁹¹(92-digit number)
14041620712678021134…58768085376982596639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.808 Γ— 10⁹¹(92-digit number)
28083241425356042269…17536170753965193279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.616 Γ— 10⁹¹(92-digit number)
56166482850712084539…35072341507930386559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.123 Γ— 10⁹²(93-digit number)
11233296570142416907…70144683015860773119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.246 Γ— 10⁹²(93-digit number)
22466593140284833815…40289366031721546239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.493 Γ— 10⁹²(93-digit number)
44933186280569667631…80578732063443092479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.986 Γ— 10⁹²(93-digit number)
89866372561139335263…61157464126886184959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.797 Γ— 10⁹³(94-digit number)
17973274512227867052…22314928253772369919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.594 Γ— 10⁹³(94-digit number)
35946549024455734105…44629856507544739839
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 163468

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 d7b5af39542c600c55e2bf67246f162772b0d7fe2e7938e3bb74aadfffc5e29f

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 #163,468 on Chainz β†—
Circulating Supply:57,648,884 XPMΒ·at block #6,800,602 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.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK