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Block #2,663,477

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/16/2018, 9:49:27 AM Β· Difficulty 11.6480 Β· 4,178,060 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8b39d0ad6c1e2bf7372553b9cfe58a1632ffb6fd125b82456768406562f03283
View on Chainz β†—

Height

#2,663,477

Difficulty

11.647959

Transactions

1

Size

200 B

Version

2

Bits

0ba5e0ac

Nonce

1,169,292,511

Timestamp

5/16/2018, 9:49:27 AM

Confirmations

4,178,060

Mined by

⛏️ P2SHAerDGUsu1J4oHHoe2e1W34LKUDoTKyXngQ

Merkle Root

eaff7464ea7d7a5348827a9bb71a512adad3d8aecd55b33b81640bdfb997a087
Transactions (1)
Coinbaseeaff7464ea7d7a…640bdfb997a087
1 in β†’ 1 out7.3600 XPM110 B
AerDGUsu…oTKyXngQ
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.

2.090 Γ— 10⁹⁡(96-digit number)
20909259435085724976…94208292974713166001
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
2.090 Γ— 10⁹⁡(96-digit number)
20909259435085724976…94208292974713166001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.181 Γ— 10⁹⁡(96-digit number)
41818518870171449952…88416585949426332001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.363 Γ— 10⁹⁡(96-digit number)
83637037740342899905…76833171898852664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.672 Γ— 10⁹⁢(97-digit number)
16727407548068579981…53666343797705328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.345 Γ— 10⁹⁢(97-digit number)
33454815096137159962…07332687595410656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.690 Γ— 10⁹⁢(97-digit number)
66909630192274319924…14665375190821312001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.338 Γ— 10⁹⁷(98-digit number)
13381926038454863984…29330750381642624001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.676 Γ— 10⁹⁷(98-digit number)
26763852076909727969…58661500763285248001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.352 Γ— 10⁹⁷(98-digit number)
53527704153819455939…17323001526570496001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.070 Γ— 10⁹⁸(99-digit number)
10705540830763891187…34646003053140992001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.141 Γ— 10⁹⁸(99-digit number)
21411081661527782375…69292006106281984001
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
Circulating Supply:57,976,679 XPMΒ·at block #6,841,536 Β· updates every 60s
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