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Block #127,629

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/21/2013, 4:05:11 PM Β· Difficulty 9.7838 Β· 6,676,285 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d178eb051f72e28867153fd558d826bd499159206b7fae7b5bcd571e176d33df
View on Chainz β†—

Height

#127,629

Difficulty

9.783821

Transactions

2

Size

2.35 KB

Version

2

Bits

09c8a87f

Nonce

248,555

Timestamp

8/21/2013, 4:05:11 PM

Confirmations

6,676,285

Mined by

⛏️ P2SHAXsfZt8c312fg4cT1Pr5J3h5wn7y4vL8NE

Merkle Root

26632b5c9a160f1553757c13e095f2e2fee47e688b0f619fd241501cee3e9362
Transactions (2)
Coinbase5d21452fc80244…47f1f7d5cbcdb9
1 in β†’ 1 out10.4600 XPM109 B
AXsfZt8c…7y4vL8NE
5ff385a854bfbe…d50abafbaa052c
19 in β†’ 1 out199.0000 XPM2.16 KB
ARArVQTd…TbA6fDTa
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.

8.095 Γ— 10⁹⁢(97-digit number)
80958485835868156903…97392861365467974601
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
8.095 Γ— 10⁹⁢(97-digit number)
80958485835868156903…97392861365467974601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.619 Γ— 10⁹⁷(98-digit number)
16191697167173631380…94785722730935949201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.238 Γ— 10⁹⁷(98-digit number)
32383394334347262761…89571445461871898401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.476 Γ— 10⁹⁷(98-digit number)
64766788668694525522…79142890923743796801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.295 Γ— 10⁹⁸(99-digit number)
12953357733738905104…58285781847487593601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.590 Γ— 10⁹⁸(99-digit number)
25906715467477810209…16571563694975187201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.181 Γ— 10⁹⁸(99-digit number)
51813430934955620418…33143127389950374401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.036 Γ— 10⁹⁹(100-digit number)
10362686186991124083…66286254779900748801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.072 Γ— 10⁹⁹(100-digit number)
20725372373982248167…32572509559801497601
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:57,675,359 XPMΒ·at block #6,803,913 Β· updates every 60s
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