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Block #123,146

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/18/2013, 9:35:23 PM Β· Difficulty 9.7613 Β· 6,672,824 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1a4fc585d53193686f3670bd1722a75af92dd471e6c12174e56710f43d592950
View on Chainz β†—

Height

#123,146

Difficulty

9.761301

Transactions

2

Size

390 B

Version

2

Bits

09c2e499

Nonce

13,369

Timestamp

8/18/2013, 9:35:23 PM

Confirmations

6,672,824

Mined by

⛏️ P2SHAZ2ybyo88cf4gMeMU8kCa47DALs67GLyYB

Merkle Root

66f6a1d599ab23093efcf4aad62e06e569f93cc5fba947613f5aca34d77ab458
Transactions (2)
Coinbasee24024071bf87d…adb6ff4daae16b
1 in β†’ 1 out10.4900 XPM109 B
AZ2ybyo8…s67GLyYB
5e0fa84efa426d…392db58c9c0d2f
1 in β†’ 2 out10.4900 XPM191 B
Aakf2i4L…8uM9aT5CAXUtFnVB…2K4kmJnq
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.

1.656 Γ— 10⁹⁴(95-digit number)
16567753092104541417…60780067842570066781
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
1.656 Γ— 10⁹⁴(95-digit number)
16567753092104541417…60780067842570066781
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.313 Γ— 10⁹⁴(95-digit number)
33135506184209082835…21560135685140133561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.627 Γ— 10⁹⁴(95-digit number)
66271012368418165671…43120271370280267121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.325 Γ— 10⁹⁡(96-digit number)
13254202473683633134…86240542740560534241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.650 Γ— 10⁹⁡(96-digit number)
26508404947367266268…72481085481121068481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.301 Γ— 10⁹⁡(96-digit number)
53016809894734532537…44962170962242136961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.060 Γ— 10⁹⁢(97-digit number)
10603361978946906507…89924341924484273921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.120 Γ— 10⁹⁢(97-digit number)
21206723957893813014…79848683848968547841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.241 Γ— 10⁹⁢(97-digit number)
42413447915787626029…59697367697937095681
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:57,611,852 XPMΒ·at block #6,795,969 Β· updates every 60s
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