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Block #103,837

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/7/2013, 6:42:03 PM Β· Difficulty 9.5393 Β· 6,691,596 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7e90aafd70899ad5d177d03fc2302a08493d20590696532900d9d38858d681d8
View on Chainz β†—

Height

#103,837

Difficulty

9.539274

Transactions

1

Size

201 B

Version

2

Bits

098a0dd7

Nonce

196,450

Timestamp

8/7/2013, 6:42:03 PM

Confirmations

6,691,596

Mined by

⛏️ P2SHAcgKcpD7BP6ggAGUVQ1r2PdZa79rx6iFP6

Merkle Root

100336a2838a388197918f515853dca11c08bf688d5c4112dea2c76437ec40f2
Transactions (1)
Coinbase100336a2838a38…a2c76437ec40f2
1 in β†’ 1 out10.9700 XPM109 B
AcgKcpD7…9rx6iFP6
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.

1.749 Γ— 10⁹⁸(99-digit number)
17499333390033622760…47496894953472744801
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
1.749 Γ— 10⁹⁸(99-digit number)
17499333390033622760…47496894953472744801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.499 Γ— 10⁹⁸(99-digit number)
34998666780067245521…94993789906945489601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.999 Γ— 10⁹⁸(99-digit number)
69997333560134491043…89987579813890979201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.399 Γ— 10⁹⁹(100-digit number)
13999466712026898208…79975159627781958401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.799 Γ— 10⁹⁹(100-digit number)
27998933424053796417…59950319255563916801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.599 Γ— 10⁹⁹(100-digit number)
55997866848107592834…19900638511127833601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.119 Γ— 10¹⁰⁰(101-digit number)
11199573369621518566…39801277022255667201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.239 Γ— 10¹⁰⁰(101-digit number)
22399146739243037133…79602554044511334401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.479 Γ— 10¹⁰⁰(101-digit number)
44798293478486074267…59205108089022668801
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:57,607,527 XPMΒ·at block #6,795,432 Β· updates every 60s
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