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Block #38,423

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2013, 12:02:28 PM Β· Difficulty 8.1813 Β· 6,777,632 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
98575acb7763a7e94f8648611e1eac2e367233a9f2590992f27d8844c16a1ab5
View on Chainz β†—

Height

#38,423

Difficulty

8.181292

Transactions

2

Size

358 B

Version

2

Bits

082e6920

Nonce

46

Timestamp

7/14/2013, 12:02:28 PM

Confirmations

6,777,632

Mined by

⛏️ P2SHASgLG4P7k4TJgNLug29X8ssFX6qzjsn9iq

Merkle Root

fe79012562b1328032344a64c5f18cc50809ce6f78d8a02a61457973da849727
Transactions (2)
Coinbasea1f2e44f73f3f1…39326f73961739
1 in β†’ 1 out14.9300 XPM110 B
ASgLG4P7…qzjsn9iq
070470c3e766c7…0d3b5263a05af2
1 in β†’ 1 out15.6400 XPM157 B
AccN9Axq…tJCNZ8bv
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.

1.481 Γ— 10⁹⁸(99-digit number)
14818526027529841426…51201721059417631499
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
1.481 Γ— 10⁹⁸(99-digit number)
14818526027529841426…51201721059417631499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.963 Γ— 10⁹⁸(99-digit number)
29637052055059682852…02403442118835262999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.927 Γ— 10⁹⁸(99-digit number)
59274104110119365705…04806884237670525999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.185 Γ— 10⁹⁹(100-digit number)
11854820822023873141…09613768475341051999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.370 Γ— 10⁹⁹(100-digit number)
23709641644047746282…19227536950682103999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.741 Γ— 10⁹⁹(100-digit number)
47419283288095492564…38455073901364207999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.483 Γ— 10⁹⁹(100-digit number)
94838566576190985129…76910147802728415999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.896 Γ— 10¹⁰⁰(101-digit number)
18967713315238197025…53820295605456831999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.793 Γ— 10¹⁰⁰(101-digit number)
37935426630476394051…07640591210913663999
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:57,772,555 XPMΒ·at block #6,816,054 Β· updates every 60s
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