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Block #127,226

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/21/2013, 9:32:35 AM Β· Difficulty 9.7833 Β· 6,682,756 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d5fbb6aff42786b84bd1c72cf168d3a600085ea05d79233a025aaebfe56db935
View on Chainz β†—

Height

#127,226

Difficulty

9.783286

Transactions

1

Size

200 B

Version

2

Bits

09c88570

Nonce

25,271

Timestamp

8/21/2013, 9:32:35 AM

Confirmations

6,682,756

Mined by

⛏️ P2SHAL4on7MoehvKsN2qMpn6JMVQDzcZpCa12j

Merkle Root

1e7e91b1404ed0177a7167e71610978ecefffb39f3f4ebb5999895e387c40268
Transactions (1)
Coinbase1e7e91b1404ed0…9895e387c40268
1 in β†’ 1 out10.4300 XPM109 B
AL4on7Mo…cZpCa12j
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.

1.943 Γ— 10⁹⁸(99-digit number)
19437344230863559654…79114667520629039921
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
1.943 Γ— 10⁹⁸(99-digit number)
19437344230863559654…79114667520629039921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.887 Γ— 10⁹⁸(99-digit number)
38874688461727119309…58229335041258079841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.774 Γ— 10⁹⁸(99-digit number)
77749376923454238618…16458670082516159681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.554 Γ— 10⁹⁹(100-digit number)
15549875384690847723…32917340165032319361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.109 Γ— 10⁹⁹(100-digit number)
31099750769381695447…65834680330064638721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.219 Γ— 10⁹⁹(100-digit number)
62199501538763390894…31669360660129277441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.243 Γ— 10¹⁰⁰(101-digit number)
12439900307752678178…63338721320258554881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.487 Γ— 10¹⁰⁰(101-digit number)
24879800615505356357…26677442640517109761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.975 Γ— 10¹⁰⁰(101-digit number)
49759601231010712715…53354885281034219521
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:57,723,928 XPMΒ·at block #6,809,981 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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