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Block #115,428

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/13/2013, 6:36:23 PM Β· Difficulty 9.7442 Β· 6,709,865 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7e9119d06a756ec62020737893f703b6988720adb99a59a66b9f4ddc7219bbbb
View on Chainz β†—

Height

#115,428

Difficulty

9.744211

Transactions

1

Size

200 B

Version

2

Bits

09be8495

Nonce

1,655

Timestamp

8/13/2013, 6:36:23 PM

Confirmations

6,709,865

Mined by

⛏️ P2SHAGELmJR6aPRjt3Z8ALYc9YsGpGUuQ4Rhjr

Merkle Root

67adef24d7b21866504128ec2695a7f712c84d948e0234138bba0638bde2830f
Transactions (1)
Coinbase67adef24d7b218…ba0638bde2830f
1 in β†’ 1 out10.5200 XPM109 B
AGELmJR6…UuQ4Rhjr
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.

2.246 Γ— 10⁹⁢(97-digit number)
22469851581222546932…99530372753693811421
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.246 Γ— 10⁹⁢(97-digit number)
22469851581222546932…99530372753693811421
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.493 Γ— 10⁹⁢(97-digit number)
44939703162445093864…99060745507387622841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.987 Γ— 10⁹⁢(97-digit number)
89879406324890187728…98121491014775245681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.797 Γ— 10⁹⁷(98-digit number)
17975881264978037545…96242982029550491361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.595 Γ— 10⁹⁷(98-digit number)
35951762529956075091…92485964059100982721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.190 Γ— 10⁹⁷(98-digit number)
71903525059912150182…84971928118201965441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.438 Γ— 10⁹⁸(99-digit number)
14380705011982430036…69943856236403930881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.876 Γ— 10⁹⁸(99-digit number)
28761410023964860073…39887712472807861761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.752 Γ— 10⁹⁸(99-digit number)
57522820047929720146…79775424945615723521
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
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