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Block #129,134

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/22/2013, 5:00:48 PM Β· Difficulty 9.7842 Β· 6,678,717 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
28475f0d5f9c83e00c50c329fa78c2d74c657b00fa9decf203effe8644c2f79a
View on Chainz β†—

Height

#129,134

Difficulty

9.784247

Transactions

2

Size

357 B

Version

2

Bits

09c8c469

Nonce

187,730

Timestamp

8/22/2013, 5:00:48 PM

Confirmations

6,678,717

Mined by

⛏️ P2SHARZi5jwJmDxjBAfjL3R8N51XBE61VgNXQh

Merkle Root

f38ca4fd600a2bc7303a9b1379eff931b6e9066993545efe10167160efcea825
Transactions (2)
Coinbasefc4514f7786891…081ae57e7e9f5b
1 in β†’ 1 out10.4400 XPM109 B
ARZi5jwJ…61VgNXQh
5ceaae3d124db0…5a1d448e6b864c
1 in β†’ 1 out10.5500 XPM157 B
AJecGVPu…Ht4pNBpS
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.

1.601 Γ— 10⁹⁢(97-digit number)
16011118165411829967…62856495673160191201
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
1.601 Γ— 10⁹⁢(97-digit number)
16011118165411829967…62856495673160191201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.202 Γ— 10⁹⁢(97-digit number)
32022236330823659934…25712991346320382401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.404 Γ— 10⁹⁢(97-digit number)
64044472661647319868…51425982692640764801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.280 Γ— 10⁹⁷(98-digit number)
12808894532329463973…02851965385281529601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.561 Γ— 10⁹⁷(98-digit number)
25617789064658927947…05703930770563059201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.123 Γ— 10⁹⁷(98-digit number)
51235578129317855894…11407861541126118401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.024 Γ— 10⁹⁸(99-digit number)
10247115625863571178…22815723082252236801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.049 Γ— 10⁹⁸(99-digit number)
20494231251727142357…45631446164504473601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.098 Γ— 10⁹⁸(99-digit number)
40988462503454284715…91262892329008947201
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:57,706,847 XPMΒ·at block #6,807,850 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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