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Block #2,943,278

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/28/2018, 5:09:41 PM Β· Difficulty 11.3938 Β· 3,900,550 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9f8ce2fd9bafd457f2aafe344cd71994bfbc08821f4589723e70a94c8d455c18
View on Chainz β†—

Height

#2,943,278

Difficulty

11.393844

Transactions

1

Size

201 B

Version

2

Bits

0b64d2ef

Nonce

1,077,527,785

Timestamp

11/28/2018, 5:09:41 PM

Confirmations

3,900,550

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

4163c4021afeb22db30f5727c16957824a5ed264042813e0cceb2de288c74132
Transactions (1)
Coinbase4163c4021afeb2…eb2de288c74132
1 in β†’ 1 out7.6900 XPM110 B
AUMQRepm…tAfKmdW1
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.

2.045 Γ— 10⁹⁢(97-digit number)
20452863576247841060…46116944073018547201
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
2.045 Γ— 10⁹⁢(97-digit number)
20452863576247841060…46116944073018547201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.090 Γ— 10⁹⁢(97-digit number)
40905727152495682121…92233888146037094401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.181 Γ— 10⁹⁢(97-digit number)
81811454304991364242…84467776292074188801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.636 Γ— 10⁹⁷(98-digit number)
16362290860998272848…68935552584148377601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.272 Γ— 10⁹⁷(98-digit number)
32724581721996545696…37871105168296755201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.544 Γ— 10⁹⁷(98-digit number)
65449163443993091393…75742210336593510401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.308 Γ— 10⁹⁸(99-digit number)
13089832688798618278…51484420673187020801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.617 Γ— 10⁹⁸(99-digit number)
26179665377597236557…02968841346374041601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.235 Γ— 10⁹⁸(99-digit number)
52359330755194473114…05937682692748083201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.047 Γ— 10⁹⁹(100-digit number)
10471866151038894622…11875365385496166401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.094 Γ— 10⁹⁹(100-digit number)
20943732302077789245…23750730770992332801
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:57,995,000 XPMΒ·at block #6,843,827 Β· updates every 60s
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