XPM Prime Explorer symbol
XPMPrime Explorer

Block #137,974

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/28/2013, 3:29:39 AM Β· Difficulty 9.8238 Β· 6,663,579 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
de0eba88b2a290438f399911379c69096747ef2890d71aff8f9c369a1e294fca
View on Chainz β†—

Height

#137,974

Difficulty

9.823754

Transactions

2

Size

1.14 KB

Version

2

Bits

09d2e18c

Nonce

36,078

Timestamp

8/28/2013, 3:29:39 AM

Confirmations

6,663,579

Mined by

⛏️ P2SHALijpL6p4BixHp8FsfSP8HJr2XpkeFex9V

Merkle Root

13734dc1bcb6627af25e7bef9bc7ebdeb5b9c582c2d0f5a7dea7a837192d4bff
Transactions (2)
Coinbase8f699a12c26f46…cbf0b10658cc03
1 in β†’ 1 out10.3600 XPM109 B
ALijpL6p…pkeFex9V
09bde58472782f…8e2d79eff754f4
6 in β†’ 2 out7.0331 XPM965 B
AS2HkKE2…gKLaJEvmAesqv4Qx…q5jvoR4s
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.

2.273 Γ— 10⁹⁡(96-digit number)
22735626366767696880…75416719931065708159
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
2.273 Γ— 10⁹⁡(96-digit number)
22735626366767696880…75416719931065708159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.547 Γ— 10⁹⁡(96-digit number)
45471252733535393761…50833439862131416319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.094 Γ— 10⁹⁡(96-digit number)
90942505467070787522…01666879724262832639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.818 Γ— 10⁹⁢(97-digit number)
18188501093414157504…03333759448525665279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.637 Γ— 10⁹⁢(97-digit number)
36377002186828315009…06667518897051330559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.275 Γ— 10⁹⁢(97-digit number)
72754004373656630018…13335037794102661119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.455 Γ— 10⁹⁷(98-digit number)
14550800874731326003…26670075588205322239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.910 Γ— 10⁹⁷(98-digit number)
29101601749462652007…53340151176410644479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.820 Γ— 10⁹⁷(98-digit number)
58203203498925304014…06680302352821288959
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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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, …
Cross-reference on Chainz Explorer
Circulating Supply:57,656,503 XPMΒ·at block #6,801,552 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