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Block #115,848

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/14/2013, 1:10:05 AM Β· Difficulty 9.7457 Β· 6,711,262 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1ff257d79c76b4212b688e85a28ece524031a3bb29569ea53947f1975761ae53
View on Chainz β†—

Height

#115,848

Difficulty

9.745667

Transactions

1

Size

199 B

Version

2

Bits

09bee402

Nonce

656,560

Timestamp

8/14/2013, 1:10:05 AM

Confirmations

6,711,262

Mined by

⛏️ P2SHAVJaZtXCr3NXSK79aMri9GXJU2gGZDZ3Yk

Merkle Root

c4878adaa87437be0d508739cd0cf6666dd0255b2a0b3bdd00807ceea546e08c
Transactions (1)
Coinbasec4878adaa87437…807ceea546e08c
1 in β†’ 1 out10.5100 XPM109 B
AVJaZtXC…gGZDZ3Yk
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.

4.088 Γ— 10⁹⁴(95-digit number)
40883554123759175919…64108205780001120099
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
4.088 Γ— 10⁹⁴(95-digit number)
40883554123759175919…64108205780001120099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.176 Γ— 10⁹⁴(95-digit number)
81767108247518351838…28216411560002240199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.635 Γ— 10⁹⁡(96-digit number)
16353421649503670367…56432823120004480399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.270 Γ— 10⁹⁡(96-digit number)
32706843299007340735…12865646240008960799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.541 Γ— 10⁹⁡(96-digit number)
65413686598014681470…25731292480017921599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.308 Γ— 10⁹⁢(97-digit number)
13082737319602936294…51462584960035843199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.616 Γ— 10⁹⁢(97-digit number)
26165474639205872588…02925169920071686399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.233 Γ— 10⁹⁢(97-digit number)
52330949278411745176…05850339840143372799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.046 Γ— 10⁹⁷(98-digit number)
10466189855682349035…11700679680286745599
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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