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Block #91,385

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/31/2013, 9:48:14 PM Β· Difficulty 9.2192 Β· 6,721,443 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7075662c2700b72dc9550121d6a710b8081d055848f9245dd292d68501b98181
View on Chainz β†—

Height

#91,385

Difficulty

9.219179

Transactions

1

Size

200 B

Version

2

Bits

09381c1f

Nonce

60,807

Timestamp

7/31/2013, 9:48:14 PM

Confirmations

6,721,443

Mined by

⛏️ P2SHAeEXQxqG1a9HUoHobjrNQ1M2oHJ2q5dxWc

Merkle Root

bafcc2f6d82cb511506e93bd50880fcd4b75435b2265d9e9f2a75199104090b8
Transactions (1)
Coinbasebafcc2f6d82cb5…a75199104090b8
1 in β†’ 1 out11.7500 XPM109 B
AeEXQxqG…J2q5dxWc
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.

6.975 Γ— 10⁹⁷(98-digit number)
69750445215016243503…71088057692611489249
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
6.975 Γ— 10⁹⁷(98-digit number)
69750445215016243503…71088057692611489249
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.395 Γ— 10⁹⁸(99-digit number)
13950089043003248700…42176115385222978499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.790 Γ— 10⁹⁸(99-digit number)
27900178086006497401…84352230770445956999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.580 Γ— 10⁹⁸(99-digit number)
55800356172012994803…68704461540891913999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.116 Γ— 10⁹⁹(100-digit number)
11160071234402598960…37408923081783827999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.232 Γ— 10⁹⁹(100-digit number)
22320142468805197921…74817846163567655999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.464 Γ— 10⁹⁹(100-digit number)
44640284937610395842…49635692327135311999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.928 Γ— 10⁹⁹(100-digit number)
89280569875220791685…99271384654270623999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.785 Γ— 10¹⁰⁰(101-digit number)
17856113975044158337…98542769308541247999
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:57,746,671 XPMΒ·at block #6,812,827 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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