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Block #3,054,182

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/15/2019, 4:59:26 PM Β· Difficulty 11.0028 Β· 3,787,323 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4294ee05aea026ab9bd4f0922b7b35a1a4f41a144a39e91ccba07912746c1a79
View on Chainz β†—

Height

#3,054,182

Difficulty

11.002850

Transactions

1

Size

200 B

Version

2

Bits

0b00bac6

Nonce

177,476,701

Timestamp

2/15/2019, 4:59:26 PM

Confirmations

3,787,323

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

3d0bd00e39c5155aa60787eb349130568138c6d613fbc390bfcc85ec19b51af7
Transactions (1)
Coinbase3d0bd00e39c515…cc85ec19b51af7
1 in β†’ 1 out8.2500 XPM109 B
AUMQRepm…tAfKmdW1
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.

7.635 Γ— 10⁹⁢(97-digit number)
76351964465038505481…80255107901339392001
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
7.635 Γ— 10⁹⁢(97-digit number)
76351964465038505481…80255107901339392001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.527 Γ— 10⁹⁷(98-digit number)
15270392893007701096…60510215802678784001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.054 Γ— 10⁹⁷(98-digit number)
30540785786015402192…21020431605357568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.108 Γ— 10⁹⁷(98-digit number)
61081571572030804385…42040863210715136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.221 Γ— 10⁹⁸(99-digit number)
12216314314406160877…84081726421430272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.443 Γ— 10⁹⁸(99-digit number)
24432628628812321754…68163452842860544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.886 Γ— 10⁹⁸(99-digit number)
48865257257624643508…36326905685721088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.773 Γ— 10⁹⁸(99-digit number)
97730514515249287016…72653811371442176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.954 Γ— 10⁹⁹(100-digit number)
19546102903049857403…45307622742884352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.909 Γ— 10⁹⁹(100-digit number)
39092205806099714806…90615245485768704001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.818 Γ— 10⁹⁹(100-digit number)
78184411612199429613…81230490971537408001
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
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