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Block #278,290

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/27/2013, 10:23:49 PM Β· Difficulty 9.9686 Β· 6,520,631 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
744b879f373c4ee5d5bea24e04ed54cd570475654741f19435a3c825ef0b1cde
View on Chainz β†—

Height

#278,290

Difficulty

9.968563

Transactions

2

Size

391 B

Version

2

Bits

09f7f3c1

Nonce

168,771

Timestamp

11/27/2013, 10:23:49 PM

Confirmations

6,520,631

Mined by

⛏️ P2SHAcNCnHU9D3JiUNWyee7VjHou7ZnWtjkYN2

Merkle Root

0c613b587129b5210033660c7a2841462f76700492d6c8cba2f16671c01486ed
Transactions (2)
Coinbase956c66fabdc39c…59fc8c7b57b69c
1 in β†’ 1 out10.0600 XPM109 B
AcNCnHU9…nWtjkYN2
9237fee66a84b5…4556bd8a7eb10e
1 in β†’ 1 out0.9800 XPM191 B
Ae18tnhj…v1jnSaEQ
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.

1.116 Γ— 10⁹⁢(97-digit number)
11167449647910247830…45573239493688862721
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
1.116 Γ— 10⁹⁢(97-digit number)
11167449647910247830…45573239493688862721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.233 Γ— 10⁹⁢(97-digit number)
22334899295820495660…91146478987377725441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.466 Γ— 10⁹⁢(97-digit number)
44669798591640991320…82292957974755450881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.933 Γ— 10⁹⁢(97-digit number)
89339597183281982640…64585915949510901761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.786 Γ— 10⁹⁷(98-digit number)
17867919436656396528…29171831899021803521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.573 Γ— 10⁹⁷(98-digit number)
35735838873312793056…58343663798043607041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.147 Γ— 10⁹⁷(98-digit number)
71471677746625586112…16687327596087214081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.429 Γ— 10⁹⁸(99-digit number)
14294335549325117222…33374655192174428161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.858 Γ— 10⁹⁸(99-digit number)
28588671098650234445…66749310384348856321
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,635,401 XPMΒ·at block #6,798,920 Β· updates every 60s
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