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Block #215,129

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/17/2013, 9:30:02 PM Β· Difficulty 9.9250 Β· 6,581,245 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3eee4e4b70b7b2c5d8605dc64d182d67b9d2c2b2710f08e9168a97572a88719b
View on Chainz β†—

Height

#215,129

Difficulty

9.924975

Transactions

2

Size

506 B

Version

2

Bits

09eccb25

Nonce

67,991

Timestamp

10/17/2013, 9:30:02 PM

Confirmations

6,581,245

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

6ef580bdfc5185bd83670b24b655b5270304f916bcd68d050a981198962472a6
Transactions (2)
Coinbase45ff947f8c322f…93deaa874cda20
1 in β†’ 1 out10.1500 XPM110 B
AbuU1HhS…JPwsJEbB
f30df65908ed47…2b9d2636f65e83
2 in β†’ 1 out10.8000 XPM306 B
AWWiYdJ1…KvnDtpKR
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.

1.072 Γ— 10⁹⁴(95-digit number)
10727481293982235140…44354505767980861441
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
1.072 Γ— 10⁹⁴(95-digit number)
10727481293982235140…44354505767980861441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.145 Γ— 10⁹⁴(95-digit number)
21454962587964470281…88709011535961722881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.290 Γ— 10⁹⁴(95-digit number)
42909925175928940562…77418023071923445761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.581 Γ— 10⁹⁴(95-digit number)
85819850351857881124…54836046143846891521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.716 Γ— 10⁹⁡(96-digit number)
17163970070371576224…09672092287693783041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.432 Γ— 10⁹⁡(96-digit number)
34327940140743152449…19344184575387566081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.865 Γ— 10⁹⁡(96-digit number)
68655880281486304899…38688369150775132161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.373 Γ— 10⁹⁢(97-digit number)
13731176056297260979…77376738301550264321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.746 Γ— 10⁹⁢(97-digit number)
27462352112594521959…54753476603100528641
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:57,614,987 XPMΒ·at block #6,796,373 Β· updates every 60s
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