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Block #2,769,544

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/28/2018, 9:34:45 PM Β· Difficulty 11.6682 Β· 4,037,170 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
77082bb88e65a2aa45e1d83d757e9e1184d84d5539bd6a6b0ad7367b6677d5dc
View on Chainz β†—

Height

#2,769,544

Difficulty

11.668230

Transactions

2

Size

834 B

Version

2

Bits

0bab1127

Nonce

1,974,198,459

Timestamp

7/28/2018, 9:34:45 PM

Confirmations

4,037,170

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

aa0b4ddf485f23a71d82f51edd05239fc409791bbc389dff488c86ce8cd98971
Transactions (2)
Coinbase8908cb4e2e874f…18759c92b6be2c
1 in β†’ 1 out7.3400 XPM110 B
AZtxQr2F…7grUWrUz
537eefac7d2c70…7c5c936ef70a8b
4 in β†’ 2 out10.0300 XPM635 B
AKD9LeNP…bQTn8mEfAViDRTXJ…aZa8NH4L
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.

2.250 Γ— 10⁹²(93-digit number)
22500437225285416127…38271157858084911921
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
2.250 Γ— 10⁹²(93-digit number)
22500437225285416127…38271157858084911921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.500 Γ— 10⁹²(93-digit number)
45000874450570832254…76542315716169823841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.000 Γ— 10⁹²(93-digit number)
90001748901141664508…53084631432339647681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.800 Γ— 10⁹³(94-digit number)
18000349780228332901…06169262864679295361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.600 Γ— 10⁹³(94-digit number)
36000699560456665803…12338525729358590721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.200 Γ— 10⁹³(94-digit number)
72001399120913331606…24677051458717181441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.440 Γ— 10⁹⁴(95-digit number)
14400279824182666321…49354102917434362881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.880 Γ— 10⁹⁴(95-digit number)
28800559648365332642…98708205834868725761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.760 Γ— 10⁹⁴(95-digit number)
57601119296730665285…97416411669737451521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.152 Γ— 10⁹⁡(96-digit number)
11520223859346133057…94832823339474903041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.304 Γ— 10⁹⁡(96-digit number)
23040447718692266114…89665646678949806081
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:57,697,810 XPMΒ·at block #6,806,713 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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