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Block #122,882

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/18/2013, 6:08:37 PM Β· Difficulty 9.7586 Β· 6,683,226 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
daa62c0f1e12bffc6261eaad2240a775657c006970bcc83aa298c1667739aa0b
View on Chainz β†—

Height

#122,882

Difficulty

9.758572

Transactions

1

Size

200 B

Version

2

Bits

09c231c1

Nonce

127,488

Timestamp

8/18/2013, 6:08:37 PM

Confirmations

6,683,226

Mined by

⛏️ P2SHAbB3aifuT9ri2zqZMbJ723U3z6wrbJL6FT

Merkle Root

7655ff56eee18d93617b3be59049ecb93838182766aae701009e6e162e7e7ae1
Transactions (1)
Coinbase7655ff56eee18d…9e6e162e7e7ae1
1 in β†’ 1 out10.4900 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.

3.365 Γ— 10⁹⁢(97-digit number)
33658340823527888174…51601617425871096321
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
3.365 Γ— 10⁹⁢(97-digit number)
33658340823527888174…51601617425871096321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.731 Γ— 10⁹⁢(97-digit number)
67316681647055776348…03203234851742192641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.346 Γ— 10⁹⁷(98-digit number)
13463336329411155269…06406469703484385281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.692 Γ— 10⁹⁷(98-digit number)
26926672658822310539…12812939406968770561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.385 Γ— 10⁹⁷(98-digit number)
53853345317644621078…25625878813937541121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.077 Γ— 10⁹⁸(99-digit number)
10770669063528924215…51251757627875082241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.154 Γ— 10⁹⁸(99-digit number)
21541338127057848431…02503515255750164481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.308 Γ— 10⁹⁸(99-digit number)
43082676254115696863…05007030511500328961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.616 Γ— 10⁹⁸(99-digit number)
86165352508231393726…10014061023000657921
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:57,692,939 XPMΒ·at block #6,806,107 Β· updates every 60s
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