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Block #70,135

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2013, 12:09:15 PM Β· Difficulty 8.9918 Β· 6,725,928 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ede140dd4bb22adbeaecb8aa87e3f1a2787a08e9197d5dddddc41fc88948b81
View on Chainz β†—

Height

#70,135

Difficulty

8.991798

Transactions

1

Size

199 B

Version

2

Bits

08fde67b

Nonce

505

Timestamp

7/20/2013, 12:09:15 PM

Confirmations

6,725,928

Mined by

⛏️ P2SHAK1JUKWLjkgQU8N3MsSKyKCPeAoPR4rN5o

Merkle Root

752d0b62bb5ca9f82092f78b5a0f09faa0049244cd9686347e0b2fae426f7521
Transactions (1)
Coinbase752d0b62bb5ca9…0b2fae426f7521
1 in β†’ 1 out12.3500 XPM110 B
AK1JUKWL…oPR4rN5o
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.

1.063 Γ— 10⁹³(94-digit number)
10638499249597554181…00597584142326174761
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
1.063 Γ— 10⁹³(94-digit number)
10638499249597554181…00597584142326174761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.127 Γ— 10⁹³(94-digit number)
21276998499195108363…01195168284652349521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.255 Γ— 10⁹³(94-digit number)
42553996998390216727…02390336569304699041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.510 Γ— 10⁹³(94-digit number)
85107993996780433455…04780673138609398081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.702 Γ— 10⁹⁴(95-digit number)
17021598799356086691…09561346277218796161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.404 Γ— 10⁹⁴(95-digit number)
34043197598712173382…19122692554437592321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.808 Γ— 10⁹⁴(95-digit number)
68086395197424346764…38245385108875184641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.361 Γ— 10⁹⁡(96-digit number)
13617279039484869352…76490770217750369281
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 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 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,612,598 XPMΒ·at block #6,796,062 Β· updates every 60s
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