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Block #1,429,316

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/26/2016, 8:12:59 PM Β· Difficulty 10.7400 Β· 5,410,393 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6ff6f65976532006339a1f63b018e846001962b5ff03b2a996e676106e33c002
View on Chainz β†—

Height

#1,429,316

Difficulty

10.740016

Transactions

1

Size

200 B

Version

2

Bits

0abd71b0

Nonce

306,912,376

Timestamp

1/26/2016, 8:12:59 PM

Confirmations

5,410,393

Mined by

⛏️ P2SHAWz2YLT5SmtPJQhvBuaW811dNxvMeQWHP4

Merkle Root

afd4d3e54d1e4c107590354761ae87e9651af37eb82e7ff59a3a5b64040ccbc6
Transactions (1)
Coinbaseafd4d3e54d1e4c…3a5b64040ccbc6
1 in β†’ 1 out8.6600 XPM109 B
AWz2YLT5…vMeQWHP4
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.

9.575 Γ— 10⁹⁡(96-digit number)
95752038904520528579…13445801731831841919
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
9.575 Γ— 10⁹⁡(96-digit number)
95752038904520528579…13445801731831841919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.915 Γ— 10⁹⁢(97-digit number)
19150407780904105715…26891603463663683839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.830 Γ— 10⁹⁢(97-digit number)
38300815561808211431…53783206927327367679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.660 Γ— 10⁹⁢(97-digit number)
76601631123616422863…07566413854654735359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.532 Γ— 10⁹⁷(98-digit number)
15320326224723284572…15132827709309470719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.064 Γ— 10⁹⁷(98-digit number)
30640652449446569145…30265655418618941439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.128 Γ— 10⁹⁷(98-digit number)
61281304898893138290…60531310837237882879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.225 Γ— 10⁹⁸(99-digit number)
12256260979778627658…21062621674475765759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.451 Γ— 10⁹⁸(99-digit number)
24512521959557255316…42125243348951531519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.902 Γ— 10⁹⁸(99-digit number)
49025043919114510632…84250486697903063039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,961,961 XPMΒ·at block #6,839,708 Β· updates every 60s
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