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Block #72,330

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 11:30:31 PM Β· Difficulty 8.9940 Β· 6,724,157 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0e15421865cc51a42ad35e2268cd19e3b840072cfe4b0d7bbe73754e43846c82
View on Chainz β†—

Height

#72,330

Difficulty

8.993984

Transactions

1

Size

201 B

Version

2

Bits

08fe75b7

Nonce

52

Timestamp

7/20/2013, 11:30:31 PM

Confirmations

6,724,157

Mined by

⛏️ P2SHAZDgU5ryLDBgQ43WTK1SQdESypdmcwdqVC

Merkle Root

54daacc1a5a59de309a27d282b1d424850b9fe434193856529ce093a6702b6d2
Transactions (1)
Coinbase54daacc1a5a59d…ce093a6702b6d2
1 in β†’ 1 out12.3400 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.

3.427 Γ— 10⁹⁢(97-digit number)
34273772043895394747…64455583614040413719
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
3.427 Γ— 10⁹⁢(97-digit number)
34273772043895394747…64455583614040413719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.854 Γ— 10⁹⁢(97-digit number)
68547544087790789494…28911167228080827439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.370 Γ— 10⁹⁷(98-digit number)
13709508817558157898…57822334456161654879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.741 Γ— 10⁹⁷(98-digit number)
27419017635116315797…15644668912323309759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.483 Γ— 10⁹⁷(98-digit number)
54838035270232631595…31289337824646619519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.096 Γ— 10⁹⁸(99-digit number)
10967607054046526319…62578675649293239039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.193 Γ— 10⁹⁸(99-digit number)
21935214108093052638…25157351298586478079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.387 Γ— 10⁹⁸(99-digit number)
43870428216186105276…50314702597172956159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.774 Γ— 10⁹⁸(99-digit number)
87740856432372210552…00629405194345912319
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:57,615,894 XPMΒ·at block #6,796,486 Β· updates every 60s
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