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Block #125,992

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/20/2013, 2:42:29 PM Β· Difficulty 9.7788 Β· 6,684,365 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2ea09840dc5acff748e0371da587ddb7c2100d97459a3c7196b91f8aef6d259a
View on Chainz β†—

Height

#125,992

Difficulty

9.778793

Transactions

1

Size

200 B

Version

2

Bits

09c75efc

Nonce

654,869

Timestamp

8/20/2013, 2:42:29 PM

Confirmations

6,684,365

Mined by

⛏️ P2SHAbB3aifuT9ri2zqZMbJ723U3z6wrbJL6FT

Merkle Root

713e2d38c324dbb3857a94beb614424a0b167fddd364baf8b861bb98b12ac291
Transactions (1)
Coinbase713e2d38c324db…61bb98b12ac291
1 in β†’ 1 out10.4400 XPM109 B
AbB3aifu…wrbJL6FT
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.

5.403 Γ— 10⁹⁷(98-digit number)
54033047814403329360…72434280676321162551
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
5.403 Γ— 10⁹⁷(98-digit number)
54033047814403329360…72434280676321162551
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.080 Γ— 10⁹⁸(99-digit number)
10806609562880665872…44868561352642325101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.161 Γ— 10⁹⁸(99-digit number)
21613219125761331744…89737122705284650201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.322 Γ— 10⁹⁸(99-digit number)
43226438251522663488…79474245410569300401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.645 Γ— 10⁹⁸(99-digit number)
86452876503045326976…58948490821138600801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.729 Γ— 10⁹⁹(100-digit number)
17290575300609065395…17896981642277201601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.458 Γ— 10⁹⁹(100-digit number)
34581150601218130790…35793963284554403201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.916 Γ— 10⁹⁹(100-digit number)
69162301202436261580…71587926569108806401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.383 Γ— 10¹⁰⁰(101-digit number)
13832460240487252316…43175853138217612801
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:57,726,930 XPMΒ·at block #6,810,356 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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