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Block #71,756

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 8:19:24 PM Β· Difficulty 8.9935 Β· 6,722,974 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e428eae168cc8d9c9d2c5a358423edf5c95d3fdfb84514bbfff5e9c0555d4112
View on Chainz β†—

Height

#71,756

Difficulty

8.993490

Transactions

1

Size

200 B

Version

2

Bits

08fe5558

Nonce

956

Timestamp

7/20/2013, 8:19:24 PM

Confirmations

6,722,974

Mined by

⛏️ P2SHAZDgU5ryLDBgQ43WTK1SQdESypdmcwdqVC

Merkle Root

3424b177e535a2d36030d3b042be95b89cfdda6649479af6a05a5d3209b44806
Transactions (1)
Coinbase3424b177e535a2…5a5d3209b44806
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.

9.932 Γ— 10⁹⁴(95-digit number)
99325816221713220800…66713982774565435849
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
9.932 Γ— 10⁹⁴(95-digit number)
99325816221713220800…66713982774565435849
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.986 Γ— 10⁹⁡(96-digit number)
19865163244342644160…33427965549130871699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.973 Γ— 10⁹⁡(96-digit number)
39730326488685288320…66855931098261743399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.946 Γ— 10⁹⁡(96-digit number)
79460652977370576640…33711862196523486799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.589 Γ— 10⁹⁢(97-digit number)
15892130595474115328…67423724393046973599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.178 Γ— 10⁹⁢(97-digit number)
31784261190948230656…34847448786093947199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.356 Γ— 10⁹⁢(97-digit number)
63568522381896461312…69694897572187894399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.271 Γ— 10⁹⁷(98-digit number)
12713704476379292262…39389795144375788799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.542 Γ— 10⁹⁷(98-digit number)
25427408952758584524…78779590288751577599
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:57,601,890 XPMΒ·at block #6,794,729 Β· updates every 60s
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