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Block #71,796

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 8:32:41 PM Β· Difficulty 8.9935 Β· 6,724,692 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2182438469409e2563ba2b00f0f5954d1401259a80454302afb28ac26cc263e0
View on Chainz β†—

Height

#71,796

Difficulty

8.993526

Transactions

1

Size

201 B

Version

2

Bits

08fe57b3

Nonce

23

Timestamp

7/20/2013, 8:32:41 PM

Confirmations

6,724,692

Mined by

⛏️ P2SHAZDgU5ryLDBgQ43WTK1SQdESypdmcwdqVC

Merkle Root

878607df9f9a85d2cec5df924a4f0228b905b2ea771d0c82622075f12136db70
Transactions (1)
Coinbase878607df9f9a85…2075f12136db70
1 in β†’ 1 out12.3500 XPM110 B
AZDgU5ry…dmcwdqVC
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.

1.802 Γ— 10⁹⁢(97-digit number)
18025177891046089817…01983573399936728259
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
1.802 Γ— 10⁹⁢(97-digit number)
18025177891046089817…01983573399936728259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.605 Γ— 10⁹⁢(97-digit number)
36050355782092179634…03967146799873456519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.210 Γ— 10⁹⁢(97-digit number)
72100711564184359268…07934293599746913039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.442 Γ— 10⁹⁷(98-digit number)
14420142312836871853…15868587199493826079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.884 Γ— 10⁹⁷(98-digit number)
28840284625673743707…31737174398987652159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.768 Γ— 10⁹⁷(98-digit number)
57680569251347487415…63474348797975304319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.153 Γ— 10⁹⁸(99-digit number)
11536113850269497483…26948697595950608639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.307 Γ— 10⁹⁸(99-digit number)
23072227700538994966…53897395191901217279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,615,903 XPMΒ·at block #6,796,487 Β· updates every 60s
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