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Block #205,562

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/12/2013, 5:55:39 AM Β· Difficulty 9.8998 Β· 6,602,640 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
124c7a2cb334d4fdaf0fbecfbfdfe1c53fb453c7fff512fa0f06014bc83b49da
View on Chainz β†—

Height

#205,562

Difficulty

9.899844

Transactions

2

Size

925 B

Version

2

Bits

09e65c2f

Nonce

108,015

Timestamp

10/12/2013, 5:55:39 AM

Confirmations

6,602,640

Mined by

⛏️ P2SHAH4bvVjhsNSnSGw6RkckioXLhymxWbm6wz

Merkle Root

f5dc8c7bef0adfc0aeb362a20e345fb59a8a64af9d94d04e9387ae51bfda57dc
Transactions (2)
Coinbaseb10e05098aded6…365b178f18d023
1 in β†’ 1 out10.2000 XPM109 B
AH4bvVjh…mxWbm6wz
a41f76a0e7f7cf…02aea01a949fdb
6 in β†’ 1 out61.4300 XPM726 B
AVFFrvyR…mhs6wrX2
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.

3.233 Γ— 10⁹⁴(95-digit number)
32337024329825434645…83399258680222368001
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
3.233 Γ— 10⁹⁴(95-digit number)
32337024329825434645…83399258680222368001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.467 Γ— 10⁹⁴(95-digit number)
64674048659650869290…66798517360444736001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.293 Γ— 10⁹⁡(96-digit number)
12934809731930173858…33597034720889472001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.586 Γ— 10⁹⁡(96-digit number)
25869619463860347716…67194069441778944001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.173 Γ— 10⁹⁡(96-digit number)
51739238927720695432…34388138883557888001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.034 Γ— 10⁹⁢(97-digit number)
10347847785544139086…68776277767115776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.069 Γ— 10⁹⁢(97-digit number)
20695695571088278173…37552555534231552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.139 Γ— 10⁹⁢(97-digit number)
41391391142176556346…75105111068463104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.278 Γ— 10⁹⁢(97-digit number)
82782782284353112692…50210222136926208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.655 Γ— 10⁹⁷(98-digit number)
16556556456870622538…00420444273852416001
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:57,709,668 XPMΒ·at block #6,808,201 Β· updates every 60s
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