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Block #2,635,857

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 9:28:39 AM Β· Difficulty 11.3444 Β· 4,201,660 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6b4f7bb702c2943318e549a95aaaac393b4a96845c7a3a0e3bebcbeb07b23d5d
View on Chainz β†—

Height

#2,635,857

Difficulty

11.344369

Transactions

1

Size

201 B

Version

2

Bits

0b582895

Nonce

1,499,299,216

Timestamp

4/29/2018, 9:28:39 AM

Confirmations

4,201,660

Mined by

⛏️ P2SHAav1Tf216C7MDmBB7tgXrdi6Zoc4C7Zgfa

Merkle Root

73badbb0c1f6b28b5618f5d34452091eca22b652bc744e2012af910e53669ead
Transactions (1)
Coinbase73badbb0c1f6b2…af910e53669ead
1 in β†’ 1 out7.7600 XPM110 B
Aav1Tf21…c4C7Zgfa
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.

1.191 Γ— 10⁹⁷(98-digit number)
11915383525535351414…20690201023799731201
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
1.191 Γ— 10⁹⁷(98-digit number)
11915383525535351414…20690201023799731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.383 Γ— 10⁹⁷(98-digit number)
23830767051070702829…41380402047599462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.766 Γ— 10⁹⁷(98-digit number)
47661534102141405658…82760804095198924801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.532 Γ— 10⁹⁷(98-digit number)
95323068204282811316…65521608190397849601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.906 Γ— 10⁹⁸(99-digit number)
19064613640856562263…31043216380795699201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.812 Γ— 10⁹⁸(99-digit number)
38129227281713124526…62086432761591398401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.625 Γ— 10⁹⁸(99-digit number)
76258454563426249053…24172865523182796801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.525 Γ— 10⁹⁹(100-digit number)
15251690912685249810…48345731046365593601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.050 Γ— 10⁹⁹(100-digit number)
30503381825370499621…96691462092731187201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.100 Γ— 10⁹⁹(100-digit number)
61006763650740999242…93382924185462374401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.220 Γ— 10¹⁰⁰(101-digit number)
12201352730148199848…86765848370924748801
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:57,944,461 XPMΒ·at block #6,837,516 Β· updates every 60s
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