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Block #227,603

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/25/2013, 11:41:00 PM Β· Difficulty 9.9370 Β· 6,571,227 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6c5a3082015a497eb621bb9ca41aedc5ee33b980d6464ebd94d93cdf869fdc5b
View on Chainz β†—

Height

#227,603

Difficulty

9.936973

Transactions

2

Size

722 B

Version

2

Bits

09efdd7c

Nonce

112,369

Timestamp

10/25/2013, 11:41:00 PM

Confirmations

6,571,227

Mined by

⛏️ P2SHARBRYiL8QjnU5zrwTmS3JgwVXJoj38gY3N

Merkle Root

607fd95e36ca974a416e26e2b6b94a3fb4b133fad81cac163faa670afe899fe6
Transactions (2)
Coinbase2c9200a7d6ffb9…925b2613a26236
1 in β†’ 1 out10.1200 XPM109 B
ARBRYiL8…oj38gY3N
ed3237736cc9a8…05ffecbad84ebf
3 in β†’ 2 out28.2036 XPM523 B
AFn2B5i8…vTSeqYToAN7ZnJS4…uHpiPac9
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.

7.764 Γ— 10⁹³(94-digit number)
77641518060737308458…67380411636870841601
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
7.764 Γ— 10⁹³(94-digit number)
77641518060737308458…67380411636870841601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.552 Γ— 10⁹⁴(95-digit number)
15528303612147461691…34760823273741683201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.105 Γ— 10⁹⁴(95-digit number)
31056607224294923383…69521646547483366401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.211 Γ— 10⁹⁴(95-digit number)
62113214448589846766…39043293094966732801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.242 Γ— 10⁹⁡(96-digit number)
12422642889717969353…78086586189933465601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.484 Γ— 10⁹⁡(96-digit number)
24845285779435938706…56173172379866931201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.969 Γ— 10⁹⁡(96-digit number)
49690571558871877413…12346344759733862401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.938 Γ— 10⁹⁡(96-digit number)
99381143117743754827…24692689519467724801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.987 Γ— 10⁹⁢(97-digit number)
19876228623548750965…49385379038935449601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.975 Γ— 10⁹⁢(97-digit number)
39752457247097501930…98770758077870899201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.950 Γ— 10⁹⁢(97-digit number)
79504914494195003861…97541516155741798401
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:57,634,670 XPMΒ·at block #6,798,829 Β· updates every 60s
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