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Block #2,655,619

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/10/2018, 8:14:38 AM Β· Difficulty 11.7041 Β· 4,183,581 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a5199163faf1e7aca7b62f3469907b87ac2c0f953987ba41952daa3f3021d18e
View on Chainz β†—

Height

#2,655,619

Difficulty

11.704056

Transactions

2

Size

721 B

Version

2

Bits

0bb43d0a

Nonce

536,973,735

Timestamp

5/10/2018, 8:14:38 AM

Confirmations

4,183,581

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

8dade712493e98badee8cf30dbc0110baac37c37715c0f917aebf0b39aa15a17
Transactions (2)
Coinbase4f7972b8ef7837…13f9c9a0d714df
1 in β†’ 1 out7.3000 XPM110 B
Adqah8zh…1WwoHJ9t
6bd696e98e6bc5…0e6bffb3bb0131
3 in β†’ 2 out11.9706 XPM521 B
AMSi4AwN…BHr5df7AAZEUWKoS…ZscSkwn4
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.

4.336 Γ— 10⁹⁡(96-digit number)
43369922701787273663…15740554317794752001
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
4.336 Γ— 10⁹⁡(96-digit number)
43369922701787273663…15740554317794752001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.673 Γ— 10⁹⁡(96-digit number)
86739845403574547327…31481108635589504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.734 Γ— 10⁹⁢(97-digit number)
17347969080714909465…62962217271179008001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.469 Γ— 10⁹⁢(97-digit number)
34695938161429818930…25924434542358016001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.939 Γ— 10⁹⁢(97-digit number)
69391876322859637861…51848869084716032001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.387 Γ— 10⁹⁷(98-digit number)
13878375264571927572…03697738169432064001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.775 Γ— 10⁹⁷(98-digit number)
27756750529143855144…07395476338864128001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.551 Γ— 10⁹⁷(98-digit number)
55513501058287710289…14790952677728256001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.110 Γ— 10⁹⁸(99-digit number)
11102700211657542057…29581905355456512001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.220 Γ— 10⁹⁸(99-digit number)
22205400423315084115…59163810710913024001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.441 Γ— 10⁹⁸(99-digit number)
44410800846630168231…18327621421826048001
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:57,957,879 XPMΒ·at block #6,839,199 Β· updates every 60s
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