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Block #2,642,994

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 10:45:55 PM Β· Difficulty 11.6702 Β· 4,193,691 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
765d7c14ee4aa1df380adf32e28db81647185aca26364de9e6de9b7fc7044222
View on Chainz β†—

Height

#2,642,994

Difficulty

11.670178

Transactions

1

Size

201 B

Version

2

Bits

0bab90d1

Nonce

550,075,159

Timestamp

5/1/2018, 10:45:55 PM

Confirmations

4,193,691

Mined by

⛏️ P2SHAdbPUnpNX46rPx1WXjknn7QXGUXtgfbt8W

Merkle Root

41efe0141524d44ba18aed344f9d91271e53cd1b4fbf29e44cfbc4fbd850392d
Transactions (1)
Coinbase41efe0141524d4…fbc4fbd850392d
1 in β†’ 1 out7.3300 XPM110 B
AdbPUnpN…Xtgfbt8W
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.

4.153 Γ— 10⁹⁷(98-digit number)
41535504333897024943…93817453593081948161
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
4.153 Γ— 10⁹⁷(98-digit number)
41535504333897024943…93817453593081948161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.307 Γ— 10⁹⁷(98-digit number)
83071008667794049886…87634907186163896321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.661 Γ— 10⁹⁸(99-digit number)
16614201733558809977…75269814372327792641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.322 Γ— 10⁹⁸(99-digit number)
33228403467117619954…50539628744655585281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.645 Γ— 10⁹⁸(99-digit number)
66456806934235239909…01079257489311170561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.329 Γ— 10⁹⁹(100-digit number)
13291361386847047981…02158514978622341121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.658 Γ— 10⁹⁹(100-digit number)
26582722773694095963…04317029957244682241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.316 Γ— 10⁹⁹(100-digit number)
53165445547388191927…08634059914489364481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.063 Γ— 10¹⁰⁰(101-digit number)
10633089109477638385…17268119828978728961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.126 Γ— 10¹⁰⁰(101-digit number)
21266178218955276770…34536239657957457921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.253 Γ— 10¹⁰⁰(101-digit number)
42532356437910553541…69072479315914915841
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:57,937,761 XPMΒ·at block #6,836,684 Β· updates every 60s
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