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Block #100,937

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/6/2013, 9:57:20 AM Β· Difficulty 9.4442 Β· 6,724,559 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d3dd2546228870df1abc9ae36c5aadd38fa3ddd1c764be4fdef633573bd2110e
View on Chainz β†—

Height

#100,937

Difficulty

9.444228

Transactions

1

Size

199 B

Version

2

Bits

0971b8e6

Nonce

891,527

Timestamp

8/6/2013, 9:57:20 AM

Confirmations

6,724,559

Mined by

⛏️ P2SHAXo35Eo6zJd8nrGjrC9HGGyKN5HR8aLhkN

Merkle Root

38c2412c8f5914d7563e9011096f2f333e2afccd9e5cc5328c998a9f2e7258ae
Transactions (1)
Coinbase38c2412c8f5914…998a9f2e7258ae
1 in β†’ 1 out11.2000 XPM109 B
AXo35Eo6…HR8aLhkN
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.

7.868 Γ— 10⁹³(94-digit number)
78683118787695028270…21146628013174909901
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
7.868 Γ— 10⁹³(94-digit number)
78683118787695028270…21146628013174909901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.573 Γ— 10⁹⁴(95-digit number)
15736623757539005654…42293256026349819801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.147 Γ— 10⁹⁴(95-digit number)
31473247515078011308…84586512052699639601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.294 Γ— 10⁹⁴(95-digit number)
62946495030156022616…69173024105399279201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.258 Γ— 10⁹⁡(96-digit number)
12589299006031204523…38346048210798558401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.517 Γ— 10⁹⁡(96-digit number)
25178598012062409046…76692096421597116801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.035 Γ— 10⁹⁡(96-digit number)
50357196024124818093…53384192843194233601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.007 Γ— 10⁹⁢(97-digit number)
10071439204824963618…06768385686388467201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.014 Γ— 10⁹⁢(97-digit number)
20142878409649927237…13536771372776934401
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
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