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Block #191,894

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/3/2013, 11:32:20 AM Β· Difficulty 9.8753 Β· 6,603,080 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2f82307e114403d47d2284009f9231c2dcd3541f00577e2c69c65c264ff33d7e
View on Chainz β†—

Height

#191,894

Difficulty

9.875268

Transactions

1

Size

197 B

Version

2

Bits

09e01198

Nonce

165,232

Timestamp

10/3/2013, 11:32:20 AM

Confirmations

6,603,080

Mined by

⛏️ P2SHAZv7gMUK2zmFgrgZXsRdjKbvvPCbiASjGW

Merkle Root

8b49837e7410d0b0a8b7736327798622e0108348092058fa4d6a79c2152501cf
Transactions (1)
Coinbase8b49837e7410d0…6a79c2152501cf
1 in β†’ 1 out10.2400 XPM109 B
AZv7gMUK…CbiASjGW
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.

6.729 Γ— 10⁸⁸(89-digit number)
67293517291542575991…82336270102438665639
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
6.729 Γ— 10⁸⁸(89-digit number)
67293517291542575991…82336270102438665639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.345 Γ— 10⁸⁹(90-digit number)
13458703458308515198…64672540204877331279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.691 Γ— 10⁸⁹(90-digit number)
26917406916617030396…29345080409754662559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.383 Γ— 10⁸⁹(90-digit number)
53834813833234060793…58690160819509325119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.076 Γ— 10⁹⁰(91-digit number)
10766962766646812158…17380321639018650239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.153 Γ— 10⁹⁰(91-digit number)
21533925533293624317…34760643278037300479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.306 Γ— 10⁹⁰(91-digit number)
43067851066587248634…69521286556074600959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.613 Γ— 10⁹⁰(91-digit number)
86135702133174497269…39042573112149201919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.722 Γ— 10⁹¹(92-digit number)
17227140426634899453…78085146224298403839
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:57,603,831 XPMΒ·at block #6,794,973 Β· updates every 60s
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