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Block #2,828,632

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/7/2018, 11:02:08 AM Β· Difficulty 11.7118 Β· 4,014,558 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4f534a4da2f52c72013da6ffb5cb2249bedfc4f35efb2da508499e622cde6071
View on Chainz β†—

Height

#2,828,632

Difficulty

11.711752

Transactions

1

Size

200 B

Version

2

Bits

0bb6355c

Nonce

49,849,705

Timestamp

9/7/2018, 11:02:08 AM

Confirmations

4,014,558

Mined by

⛏️ P2SHALf5d1S88cPh89cDUdmHcTBYEKnUeiWvs9

Merkle Root

b7e87f6df3ea60fcffe1883d1a1b9ca61a372cdc01e39006764082eab19650cd
Transactions (1)
Coinbaseb7e87f6df3ea60…4082eab19650cd
1 in β†’ 1 out7.2800 XPM110 B
ALf5d1S8…nUeiWvs9
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.

3.759 Γ— 10⁹⁴(95-digit number)
37594244308308516300…52330519684886121751
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
3.759 Γ— 10⁹⁴(95-digit number)
37594244308308516300…52330519684886121751
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.518 Γ— 10⁹⁴(95-digit number)
75188488616617032601…04661039369772243501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.503 Γ— 10⁹⁡(96-digit number)
15037697723323406520…09322078739544487001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.007 Γ— 10⁹⁡(96-digit number)
30075395446646813040…18644157479088974001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.015 Γ— 10⁹⁡(96-digit number)
60150790893293626081…37288314958177948001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.203 Γ— 10⁹⁢(97-digit number)
12030158178658725216…74576629916355896001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.406 Γ— 10⁹⁢(97-digit number)
24060316357317450432…49153259832711792001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.812 Γ— 10⁹⁢(97-digit number)
48120632714634900864…98306519665423584001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.624 Γ— 10⁹⁢(97-digit number)
96241265429269801729…96613039330847168001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.924 Γ— 10⁹⁷(98-digit number)
19248253085853960345…93226078661694336001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.849 Γ— 10⁹⁷(98-digit number)
38496506171707920691…86452157323388672001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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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