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Block #71,597

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 7:31:54 PM Β· Difficulty 8.9933 Β· 6,743,437 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b782363a6e17243c24ecc77e24f63dc52b681a1a383dd226385671198d6dcaab
View on Chainz β†—

Height

#71,597

Difficulty

8.993339

Transactions

1

Size

200 B

Version

2

Bits

08fe4b7e

Nonce

398

Timestamp

7/20/2013, 7:31:54 PM

Confirmations

6,743,437

Mined by

⛏️ P2SHAH7Eh9GYMSnm23owcXVdfkeuiPK86X1CDg

Merkle Root

74875e8cce32ff0158a469c3aec16828b1355aacc8c728508ab1277396029a50
Transactions (1)
Coinbase74875e8cce32ff…b1277396029a50
1 in β†’ 1 out12.3500 XPM110 B
AH7Eh9GY…K86X1CDg
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.

4.170 Γ— 10⁹⁴(95-digit number)
41704828030362819050…67969750157539100059
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
4.170 Γ— 10⁹⁴(95-digit number)
41704828030362819050…67969750157539100059
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.340 Γ— 10⁹⁴(95-digit number)
83409656060725638100…35939500315078200119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.668 Γ— 10⁹⁡(96-digit number)
16681931212145127620…71879000630156400239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.336 Γ— 10⁹⁡(96-digit number)
33363862424290255240…43758001260312800479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.672 Γ— 10⁹⁡(96-digit number)
66727724848580510480…87516002520625600959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.334 Γ— 10⁹⁢(97-digit number)
13345544969716102096…75032005041251201919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.669 Γ— 10⁹⁢(97-digit number)
26691089939432204192…50064010082502403839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.338 Γ— 10⁹⁢(97-digit number)
53382179878864408384…00128020165004807679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.067 Γ— 10⁹⁷(98-digit number)
10676435975772881676…00256040330009615359
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:57,764,362 XPMΒ·at block #6,815,033 Β· updates every 60s
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