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Block #2,633,245

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 8:31:06 AM Β· Difficulty 11.1821 Β· 4,207,782 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b0d107c633699b47c0acdcc972fd930ed5c2cdb64a17c9eb6a5d853c68c48de3
View on Chainz β†—

Height

#2,633,245

Difficulty

11.182087

Transactions

2

Size

4.17 KB

Version

2

Bits

0b2e9d3f

Nonce

637,435,449

Timestamp

4/28/2018, 8:31:06 AM

Confirmations

4,207,782

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

c77edd267fc39ed9cb081a1729c1e8d6e512270dbad844721e7d92143d9bcda2
Transactions (2)
Coinbase535cf66d5078f3…ec625b03b88e9e
1 in β†’ 1 out8.0300 XPM110 B
Adqah8zh…1WwoHJ9t
68c4474de67730…56a18f536c4677
27 in β†’ 2 out99.9109 XPM3.98 KB
AKB6o2kc…1WP7ixkuAbpCFGyE…SHHADSHk
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.

6.606 Γ— 10⁹³(94-digit number)
66063225787520773411…89773828693649179151
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
6.606 Γ— 10⁹³(94-digit number)
66063225787520773411…89773828693649179151
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.321 Γ— 10⁹⁴(95-digit number)
13212645157504154682…79547657387298358301
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.642 Γ— 10⁹⁴(95-digit number)
26425290315008309364…59095314774596716601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.285 Γ— 10⁹⁴(95-digit number)
52850580630016618729…18190629549193433201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.057 Γ— 10⁹⁡(96-digit number)
10570116126003323745…36381259098386866401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.114 Γ— 10⁹⁡(96-digit number)
21140232252006647491…72762518196773732801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.228 Γ— 10⁹⁡(96-digit number)
42280464504013294983…45525036393547465601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.456 Γ— 10⁹⁡(96-digit number)
84560929008026589966…91050072787094931201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.691 Γ— 10⁹⁢(97-digit number)
16912185801605317993…82100145574189862401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.382 Γ— 10⁹⁢(97-digit number)
33824371603210635986…64200291148379724801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.764 Γ— 10⁹⁢(97-digit number)
67648743206421271973…28400582296759449601
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:57,972,574 XPMΒ·at block #6,841,026 Β· updates every 60s
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