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Block #49,526

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/15/2013, 8:48:02 PM Β· Difficulty 8.8666 Β· 6,745,487 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
caf05bdbe695fdfbea1f8f9ca39ab023ea43b8e901486860085e36f7688065f5
View on Chainz β†—

Height

#49,526

Difficulty

8.866574

Transactions

1

Size

200 B

Version

2

Bits

08ddd7cc

Nonce

471

Timestamp

7/15/2013, 8:48:02 PM

Confirmations

6,745,487

Mined by

⛏️ P2SHARAbwBo5yscDhXRAR3dbV4NFoY367Zk7v8

Merkle Root

e747423869952ab12f1025c2b9820135c054ea2a5cc08937c3898356a1b272f3
Transactions (1)
Coinbasee747423869952a…898356a1b272f3
1 in β†’ 1 out12.7000 XPM110 B
ARAbwBo5…367Zk7v8
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.

7.615 Γ— 10⁹⁡(96-digit number)
76156862867472853055…60639664924436742969
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
7.615 Γ— 10⁹⁡(96-digit number)
76156862867472853055…60639664924436742969
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.523 Γ— 10⁹⁢(97-digit number)
15231372573494570611…21279329848873485939
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.046 Γ— 10⁹⁢(97-digit number)
30462745146989141222…42558659697746971879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.092 Γ— 10⁹⁢(97-digit number)
60925490293978282444…85117319395493943759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.218 Γ— 10⁹⁷(98-digit number)
12185098058795656488…70234638790987887519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.437 Γ— 10⁹⁷(98-digit number)
24370196117591312977…40469277581975775039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.874 Γ— 10⁹⁷(98-digit number)
48740392235182625955…80938555163951550079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.748 Γ— 10⁹⁷(98-digit number)
97480784470365251911…61877110327903100159
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:57,604,149 XPMΒ·at block #6,795,012 Β· updates every 60s
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