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Block #2,643,254

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 1:05:40 AM Β· Difficulty 11.6780 Β· 4,189,430 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
30f1a4b9b4da692fcea5ec1a57c98755f13f1a5071d3c542cc0ed878bf22d404
View on Chainz β†—

Height

#2,643,254

Difficulty

11.677977

Transactions

1

Size

201 B

Version

2

Bits

0bad8fed

Nonce

810,902,400

Timestamp

5/2/2018, 1:05:40 AM

Confirmations

4,189,430

Mined by

⛏️ P2SHAVX247EC3fhKjPbE9UG1CYDeWfvHhUac65

Merkle Root

11dbc6e9e942723ebfd1f8ee8d5fe430f8ee5778b0d697eecbe3e01a20f162c9
Transactions (1)
Coinbase11dbc6e9e94272…e3e01a20f162c9
1 in β†’ 1 out7.3200 XPM110 B
AVX247EC…vHhUac65
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.

5.990 Γ— 10⁹⁢(97-digit number)
59904471024681893491…98766754585057208321
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
5.990 Γ— 10⁹⁢(97-digit number)
59904471024681893491…98766754585057208321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.198 Γ— 10⁹⁷(98-digit number)
11980894204936378698…97533509170114416641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.396 Γ— 10⁹⁷(98-digit number)
23961788409872757396…95067018340228833281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.792 Γ— 10⁹⁷(98-digit number)
47923576819745514793…90134036680457666561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.584 Γ— 10⁹⁷(98-digit number)
95847153639491029587…80268073360915333121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.916 Γ— 10⁹⁸(99-digit number)
19169430727898205917…60536146721830666241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.833 Γ— 10⁹⁸(99-digit number)
38338861455796411834…21072293443661332481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.667 Γ— 10⁹⁸(99-digit number)
76677722911592823669…42144586887322664961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.533 Γ— 10⁹⁹(100-digit number)
15335544582318564733…84289173774645329921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.067 Γ— 10⁹⁹(100-digit number)
30671089164637129467…68578347549290659841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.134 Γ— 10⁹⁹(100-digit number)
61342178329274258935…37156695098581319681
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:57,905,627 XPMΒ·at block #6,832,683 Β· updates every 60s
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