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Block #30,735

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/13/2013, 8:26:48 PM Β· Difficulty 7.9874 Β· 6,779,340 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
af19c9dd471180c46ba6790992588adcccf5ca9c0222488df2dad59fe2310610
View on Chainz β†—

Height

#30,735

Difficulty

7.987430

Transactions

1

Size

198 B

Version

2

Bits

07fcc83b

Nonce

45

Timestamp

7/13/2013, 8:26:48 PM

Confirmations

6,779,340

Mined by

⛏️ P2SHAGemJXng9Py5jf5TzegELEhNUUw1K3MEut

Merkle Root

bb6b22fd82f6849f1b309f8e79bd6194d8d25e21580526f0cf34637463ad3031
Transactions (1)
Coinbasebb6b22fd82f684…34637463ad3031
1 in β†’ 1 out15.6500 XPM108 B
AGemJXng…w1K3MEut
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.

2.755 Γ— 10⁹⁴(95-digit number)
27554476351864302054…67407309463431053441
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
2.755 Γ— 10⁹⁴(95-digit number)
27554476351864302054…67407309463431053441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.510 Γ— 10⁹⁴(95-digit number)
55108952703728604109…34814618926862106881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.102 Γ— 10⁹⁡(96-digit number)
11021790540745720821…69629237853724213761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.204 Γ— 10⁹⁡(96-digit number)
22043581081491441643…39258475707448427521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.408 Γ— 10⁹⁡(96-digit number)
44087162162982883287…78516951414896855041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.817 Γ— 10⁹⁡(96-digit number)
88174324325965766574…57033902829793710081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.763 Γ— 10⁹⁢(97-digit number)
17634864865193153314…14067805659587420161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.526 Γ— 10⁹⁢(97-digit number)
35269729730386306629…28135611319174840321
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:57,724,671 XPMΒ·at block #6,810,074 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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