XPM Prime Explorer symbol
XPMPrime Explorer

Block #73,126

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 4:03:48 AM Β· Difficulty 8.9946 Β· 6,723,524 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
199470ede051ed0250a459f1d21bd37f9565b09ed1b0745e78fecd104223257a
View on Chainz β†—

Height

#73,126

Difficulty

8.994599

Transactions

1

Size

197 B

Version

2

Bits

08fe9e07

Nonce

621

Timestamp

7/21/2013, 4:03:48 AM

Confirmations

6,723,524

Mined by

⛏️ P2SHAeVvGUh4cnFPF4FMDsxtGiaqQhkYpQ2wDQ

Merkle Root

224f0183b2ea4b6b57f06e9fa77336da05c5d4f5be42c44074698b9f8d99123f
Transactions (1)
Coinbase224f0183b2ea4b…698b9f8d99123f
1 in β†’ 1 out12.3400 XPM110 B
AeVvGUh4…kYpQ2wDQ
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.

1.542 Γ— 10⁸⁷(88-digit number)
15424124441891339866…52248517377591950101
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.542 Γ— 10⁸⁷(88-digit number)
15424124441891339866…52248517377591950101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.084 Γ— 10⁸⁷(88-digit number)
30848248883782679732…04497034755183900201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.169 Γ— 10⁸⁷(88-digit number)
61696497767565359465…08994069510367800401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.233 Γ— 10⁸⁸(89-digit number)
12339299553513071893…17988139020735600801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.467 Γ— 10⁸⁸(89-digit number)
24678599107026143786…35976278041471201601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.935 Γ— 10⁸⁸(89-digit number)
49357198214052287572…71952556082942403201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.871 Γ— 10⁸⁸(89-digit number)
98714396428104575144…43905112165884806401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.974 Γ— 10⁸⁹(90-digit number)
19742879285620915028…87810224331769612801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.948 Γ— 10⁸⁹(90-digit number)
39485758571241830057…75620448663539225601
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,617,203 XPMΒ·at block #6,796,649 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