XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #127,530

Block #127,530

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/21/2013, 2:25:11 PM Β· Difficulty 9.7838 Β· 6,668,855 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6dbb25f1501d515ff2b4cd73eb4efb8c58ad0ee5e773d45b04e0f3cdebb6b2cf
View on Chainz β†—

Height

#127,530

Difficulty

9.783823

Transactions

2

Size

1.14 KB

Version

2

Bits

09c8a89f

Nonce

116,151

Timestamp

8/21/2013, 2:25:11 PM

Confirmations

6,668,855

Merkle Root

b0b1da081835322273d62dcb8ff058ffa0b066b07495a8d4df1737dbcec0cce4
Transactions (2)
Coinbasee5ddf14ae783c3…388ccb036e77d3
1 in β†’ 1 out10.4400 XPM109 B
APQA2UNx…h7jnN7FG
2c25ddb4fe19dd…5af750425097e0
6 in β†’ 2 out2.0176 XPM970 B
ANvqUEu4…W1B41M2LAHzxAdBT…pXaksKA4
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.

2.322 Γ— 10⁹⁸(99-digit number)
23225077682535018970…12312217525675767010
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
2.322 Γ— 10⁹⁸(99-digit number)
23225077682535018970…12312217525675767009
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.645 Γ— 10⁹⁸(99-digit number)
46450155365070037940…24624435051351534019
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.290 Γ— 10⁹⁸(99-digit number)
92900310730140075881…49248870102703068039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.858 Γ— 10⁹⁹(100-digit number)
18580062146028015176…98497740205406136079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.716 Γ— 10⁹⁹(100-digit number)
37160124292056030352…96995480410812272159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.432 Γ— 10⁹⁹(100-digit number)
74320248584112060704…93990960821624544319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.486 Γ— 10¹⁰⁰(101-digit number)
14864049716822412140…87981921643249088639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.972 Γ— 10¹⁰⁰(101-digit number)
29728099433644824281…75963843286498177279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.945 Γ— 10¹⁰⁰(101-digit number)
59456198867289648563…51927686572996354559
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 127530

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 6dbb25f1501d515ff2b4cd73eb4efb8c58ad0ee5e773d45b04e0f3cdebb6b2cf

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 #127,530 on Chainz β†—
Circulating Supply:57,615,077 XPMΒ·at block #6,796,384 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