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Block #97,970

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/5/2013, 12:24:51 AM Β· Difficulty 9.3242 Β· 6,718,618 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e93859c8fdbd52a9b43a79a992434a9768f7850e48ea722cc2d258fd17bcb82b
View on Chainz β†—

Height

#97,970

Difficulty

9.324165

Transactions

1

Size

199 B

Version

2

Bits

0952fc76

Nonce

391,207

Timestamp

8/5/2013, 12:24:51 AM

Confirmations

6,718,618

Mined by

⛏️ P2SHAXvMMum1Pa5kWMWJFC5uKC4CTEy1ajpFRb

Merkle Root

f940f16cbb14f40f5df2c26ebb77c08b1f0ccc5bce5320b1f8da085ec6970fbf
Transactions (1)
Coinbasef940f16cbb14f4…da085ec6970fbf
1 in β†’ 1 out11.4900 XPM109 B
AXvMMum1…y1ajpFRb
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.

1.414 Γ— 10⁹⁴(95-digit number)
14144459235434642179…95796437042862476459
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
1.414 Γ— 10⁹⁴(95-digit number)
14144459235434642179…95796437042862476459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.828 Γ— 10⁹⁴(95-digit number)
28288918470869284359…91592874085724952919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.657 Γ— 10⁹⁴(95-digit number)
56577836941738568719…83185748171449905839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.131 Γ— 10⁹⁡(96-digit number)
11315567388347713743…66371496342899811679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.263 Γ— 10⁹⁡(96-digit number)
22631134776695427487…32742992685799623359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.526 Γ— 10⁹⁡(96-digit number)
45262269553390854975…65485985371599246719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.052 Γ— 10⁹⁡(96-digit number)
90524539106781709951…30971970743198493439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.810 Γ— 10⁹⁢(97-digit number)
18104907821356341990…61943941486396986879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.620 Γ— 10⁹⁢(97-digit number)
36209815642712683980…23887882972793973759
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
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