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Block #2,634,077

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 6:15:09 PM Β· Difficulty 11.2214 Β· 4,209,961 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0472748837491a755edcd9be31236e1c49da8e9dd60bdae30e377299aa17b133
View on Chainz β†—

Height

#2,634,077

Difficulty

11.221435

Transactions

1

Size

201 B

Version

2

Bits

0b38aff4

Nonce

85,949,287

Timestamp

4/28/2018, 6:15:09 PM

Confirmations

4,209,961

Mined by

⛏️ P2SHAWU9QT1MT14XK7FyMALMWoLKhuTXfGqJcJ

Merkle Root

60ce53533e1b3a8eb22e7e27939147ab5c99ef3991bc24a936e41efabc07ba7c
Transactions (1)
Coinbase60ce53533e1b3a…e41efabc07ba7c
1 in β†’ 1 out7.9300 XPM110 B
AWU9QT1M…TXfGqJcJ
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.

4.244 Γ— 10⁹⁢(97-digit number)
42445225362739853623…55491802156488981761
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
4.244 Γ— 10⁹⁢(97-digit number)
42445225362739853623…55491802156488981761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.489 Γ— 10⁹⁢(97-digit number)
84890450725479707247…10983604312977963521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.697 Γ— 10⁹⁷(98-digit number)
16978090145095941449…21967208625955927041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.395 Γ— 10⁹⁷(98-digit number)
33956180290191882899…43934417251911854081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.791 Γ— 10⁹⁷(98-digit number)
67912360580383765798…87868834503823708161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.358 Γ— 10⁹⁸(99-digit number)
13582472116076753159…75737669007647416321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.716 Γ— 10⁹⁸(99-digit number)
27164944232153506319…51475338015294832641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.432 Γ— 10⁹⁸(99-digit number)
54329888464307012638…02950676030589665281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.086 Γ— 10⁹⁹(100-digit number)
10865977692861402527…05901352061179330561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.173 Γ— 10⁹⁹(100-digit number)
21731955385722805055…11802704122358661121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.346 Γ— 10⁹⁹(100-digit number)
43463910771445610110…23605408244717322241
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:57,996,682 XPMΒ·at block #6,844,037 Β· updates every 60s
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