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Block #3,054,180

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/15/2019, 4:58:12 PM Β· Difficulty 11.0028 Β· 3,786,996 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a4bb36a84e34284d5c87db5b40b1cf4fc6cd5237daeb9f5d4888cfdfc3f74b4b
View on Chainz β†—

Height

#3,054,180

Difficulty

11.002797

Transactions

1

Size

200 B

Version

2

Bits

0b00b750

Nonce

1,124,422,383

Timestamp

2/15/2019, 4:58:12 PM

Confirmations

3,786,996

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

821d6d82cf75f6d354a71d691fcea9a67eee0d5201efbe2cd80bbac63ea23d13
Transactions (1)
Coinbase821d6d82cf75f6…0bbac63ea23d13
1 in β†’ 1 out8.2500 XPM110 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.

7.646 Γ— 10⁹⁴(95-digit number)
76468269492137466797…83960313095913369601
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
7.646 Γ— 10⁹⁴(95-digit number)
76468269492137466797…83960313095913369601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.529 Γ— 10⁹⁡(96-digit number)
15293653898427493359…67920626191826739201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.058 Γ— 10⁹⁡(96-digit number)
30587307796854986719…35841252383653478401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.117 Γ— 10⁹⁡(96-digit number)
61174615593709973438…71682504767306956801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.223 Γ— 10⁹⁢(97-digit number)
12234923118741994687…43365009534613913601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.446 Γ— 10⁹⁢(97-digit number)
24469846237483989375…86730019069227827201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.893 Γ— 10⁹⁢(97-digit number)
48939692474967978750…73460038138455654401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.787 Γ— 10⁹⁢(97-digit number)
97879384949935957501…46920076276911308801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.957 Γ— 10⁹⁷(98-digit number)
19575876989987191500…93840152553822617601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.915 Γ— 10⁹⁷(98-digit number)
39151753979974383000…87680305107645235201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.830 Γ— 10⁹⁷(98-digit number)
78303507959948766001…75360610215290470401
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:57,973,766 XPMΒ·at block #6,841,175 Β· updates every 60s
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