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Block #251,558

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/9/2013, 2:26:05 AM Β· Difficulty 9.9700 Β· 6,547,032 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e14ed1a53d43dd3915fc9f993e225eb51bd1672f302095d1f300fc34bd65876b
View on Chainz β†—

Height

#251,558

Difficulty

9.970016

Transactions

2

Size

64.15 KB

Version

2

Bits

09f852f0

Nonce

79,076

Timestamp

11/9/2013, 2:26:05 AM

Confirmations

6,547,032

Mined by

⛏️ P2SHAaXb6LdzMFohbBjmNyta5dnWNNXefG91jF

Merkle Root

2d7fbc289e2cbaa4d8843aa3343e13935a07f8dfb2aae3edf245aca7927f1cd6
Transactions (2)
Coinbasef89aa582215e09…81b0eb44a7899f
1 in β†’ 1 out10.7800 XPM100 B
AaXb6Ldz…XefG91jF
f49d5768ab84ec…b10cd14447438d
442 in β†’ 2 out50.0100 XPM63.96 KB
AZ3CWQqM…jzD9pRSnAFsuc4C9…Bf13bsiN
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.

3.260 Γ— 10⁹³(94-digit number)
32609272369167142132…42727701258171142001
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
3.260 Γ— 10⁹³(94-digit number)
32609272369167142132…42727701258171142001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.521 Γ— 10⁹³(94-digit number)
65218544738334284265…85455402516342284001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.304 Γ— 10⁹⁴(95-digit number)
13043708947666856853…70910805032684568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.608 Γ— 10⁹⁴(95-digit number)
26087417895333713706…41821610065369136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.217 Γ— 10⁹⁴(95-digit number)
52174835790667427412…83643220130738272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.043 Γ— 10⁹⁡(96-digit number)
10434967158133485482…67286440261476544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.086 Γ— 10⁹⁡(96-digit number)
20869934316266970964…34572880522953088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.173 Γ— 10⁹⁡(96-digit number)
41739868632533941929…69145761045906176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.347 Γ— 10⁹⁡(96-digit number)
83479737265067883859…38291522091812352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.669 Γ— 10⁹⁢(97-digit number)
16695947453013576771…76583044183624704001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,632,733 XPMΒ·at block #6,798,589 Β· updates every 60s
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