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Block #248,532

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/7/2013, 10:50:30 AM Β· Difficulty 9.9658 Β· 6,556,642 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4fd04f53b3744d5180d4ad9e4997c264426cf5478cf78f923fa06b773b1587b4
View on Chainz β†—

Height

#248,532

Difficulty

9.965772

Transactions

1

Size

198 B

Version

2

Bits

09f73cd0

Nonce

13,536

Timestamp

11/7/2013, 10:50:30 AM

Confirmations

6,556,642

Mined by

⛏️ P2SHAPK6TsLc8JxWgj41xMVz2y8mnfkbATRbnm

Merkle Root

ebcfdca01854084dd5650e9d89a8c9277e7cf4b0f9698c4b552d9cce3996382d
Transactions (1)
Coinbaseebcfdca0185408…2d9cce3996382d
1 in β†’ 1 out10.0500 XPM109 B
APK6TsLc…kbATRbnm
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.

1.161 Γ— 10⁹³(94-digit number)
11611220285475866255…02128323766131786251
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
1.161 Γ— 10⁹³(94-digit number)
11611220285475866255…02128323766131786251
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.322 Γ— 10⁹³(94-digit number)
23222440570951732511…04256647532263572501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.644 Γ— 10⁹³(94-digit number)
46444881141903465023…08513295064527145001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.288 Γ— 10⁹³(94-digit number)
92889762283806930046…17026590129054290001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.857 Γ— 10⁹⁴(95-digit number)
18577952456761386009…34053180258108580001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.715 Γ— 10⁹⁴(95-digit number)
37155904913522772018…68106360516217160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.431 Γ— 10⁹⁴(95-digit number)
74311809827045544037…36212721032434320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.486 Γ— 10⁹⁡(96-digit number)
14862361965409108807…72425442064868640001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.972 Γ— 10⁹⁡(96-digit number)
29724723930818217614…44850884129737280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.944 Γ— 10⁹⁡(96-digit number)
59449447861636435229…89701768259474560001
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:57,685,460 XPMΒ·at block #6,805,173 Β· updates every 60s
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