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Block #28,386

1CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2013, 12:07:26 PM Β· Difficulty 7.9818 Β· 6,781,835 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
70b861864bf9feabd0ba1192f361217b302d83db8ccca532219bd7d221398fcc
View on Chainz β†—

Height

#28,386

Difficulty

7.981772

Transactions

1

Size

199 B

Version

2

Bits

07fb5570

Nonce

124

Timestamp

7/13/2013, 12:07:26 PM

Confirmations

6,781,835

Mined by

⛏️ P2SHAKSwr9eUsXtYAeGKZ6MmF96jvsdLNxuVyn

Merkle Root

c5618f5bada5a3642940a8f9f96940ea81c5535d8f613be14ebf75b420c4494d
Transactions (1)
Coinbasec5618f5bada5a3…bf75b420c4494d
1 in β†’ 1 out15.6800 XPM109 B
AKSwr9eU…dLNxuVyn
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.

2.029 Γ— 10⁹⁴(95-digit number)
20298370933891903501…98808165335252926749
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
2.029 Γ— 10⁹⁴(95-digit number)
20298370933891903501…98808165335252926749
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.059 Γ— 10⁹⁴(95-digit number)
40596741867783807002…97616330670505853499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.119 Γ— 10⁹⁴(95-digit number)
81193483735567614004…95232661341011706999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.623 Γ— 10⁹⁡(96-digit number)
16238696747113522800…90465322682023413999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.247 Γ— 10⁹⁡(96-digit number)
32477393494227045601…80930645364046827999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.495 Γ— 10⁹⁡(96-digit number)
64954786988454091203…61861290728093655999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.299 Γ— 10⁹⁢(97-digit number)
12990957397690818240…23722581456187311999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,725,843 XPMΒ·at block #6,810,220 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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