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Block #159,220

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2013, 10:59:58 PM Β· Difficulty 9.8661 Β· 6,645,876 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4970da6107bb1e1783b8ea4163462a9e76486fc7f678e4c5f61b2aa1f3bf0093
View on Chainz β†—

Height

#159,220

Difficulty

9.866094

Transactions

1

Size

199 B

Version

2

Bits

09ddb85d

Nonce

68,982

Timestamp

9/10/2013, 10:59:58 PM

Confirmations

6,645,876

Mined by

⛏️ P2SHATpY3yjGz2VkvD9ouyCLzJKmJFxZyYqhas

Merkle Root

7058a8d46f1500e374c0549030603fedc1706da55fa22f8784f557a3af25ab55
Transactions (1)
Coinbase7058a8d46f1500…f557a3af25ab55
1 in β†’ 1 out10.2600 XPM109 B
ATpY3yjG…xZyYqhas
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.

2.915 Γ— 10⁹⁡(96-digit number)
29154075009476708348…49135084921638033761
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
2.915 Γ— 10⁹⁡(96-digit number)
29154075009476708348…49135084921638033761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.830 Γ— 10⁹⁡(96-digit number)
58308150018953416697…98270169843276067521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.166 Γ— 10⁹⁢(97-digit number)
11661630003790683339…96540339686552135041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.332 Γ— 10⁹⁢(97-digit number)
23323260007581366678…93080679373104270081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.664 Γ— 10⁹⁢(97-digit number)
46646520015162733357…86161358746208540161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.329 Γ— 10⁹⁢(97-digit number)
93293040030325466715…72322717492417080321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.865 Γ— 10⁹⁷(98-digit number)
18658608006065093343…44645434984834160641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.731 Γ— 10⁹⁷(98-digit number)
37317216012130186686…89290869969668321281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.463 Γ— 10⁹⁷(98-digit number)
74634432024260373372…78581739939336642561
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,684,834 XPMΒ·at block #6,805,095 Β· updates every 60s
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