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Block #58,272

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/17/2013, 7:47:24 PM Β· Difficulty 8.9590 Β· 6,769,018 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5eddc3566c3fe43b50ce52bb51deb4c06e652086418b5e5cc8e39ac89fd8f9a2
View on Chainz β†—

Height

#58,272

Difficulty

8.958991

Transactions

1

Size

199 B

Version

2

Bits

08f58068

Nonce

393

Timestamp

7/17/2013, 7:47:24 PM

Confirmations

6,769,018

Mined by

⛏️ P2SHAPnz4kGcar5CWKgiJywxxfH4P6qXozup97

Merkle Root

bf676afeeecc45d271c4fe57550668d8ec07a4eea3571a3623b2322478f53310
Transactions (1)
Coinbasebf676afeeecc45…b2322478f53310
1 in β†’ 1 out12.4400 XPM109 B
APnz4kGc…qXozup97
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.

7.318 Γ— 10⁹³(94-digit number)
73181979850473629151…25374637667360089091
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
7.318 Γ— 10⁹³(94-digit number)
73181979850473629151…25374637667360089091
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.463 Γ— 10⁹⁴(95-digit number)
14636395970094725830…50749275334720178181
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.927 Γ— 10⁹⁴(95-digit number)
29272791940189451660…01498550669440356361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.854 Γ— 10⁹⁴(95-digit number)
58545583880378903321…02997101338880712721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.170 Γ— 10⁹⁡(96-digit number)
11709116776075780664…05994202677761425441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.341 Γ— 10⁹⁡(96-digit number)
23418233552151561328…11988405355522850881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.683 Γ— 10⁹⁡(96-digit number)
46836467104303122657…23976810711045701761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.367 Γ— 10⁹⁡(96-digit number)
93672934208606245314…47953621422091403521
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:57,862,429 XPMΒ·at block #6,827,289 Β· updates every 60s
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