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Block #153,120

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/6/2013, 7:06:28 PM Β· Difficulty 9.8631 Β· 6,655,892 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2b3dc54e889f7db0156b5002040b67bad6dc9bcf1af29cca41520cedf13190f2
View on Chainz β†—

Height

#153,120

Difficulty

9.863063

Transactions

1

Size

199 B

Version

2

Bits

09dcf1ac

Nonce

387,658

Timestamp

9/6/2013, 7:06:28 PM

Confirmations

6,655,892

Mined by

⛏️ P2SHARzKAGFyC84BWrrsxzVJMjM6R6E5bJQ6Gf

Merkle Root

fc8571107d45791752810cd20229b79f12be895576d189aa15b7a3ab72d4f5ee
Transactions (1)
Coinbasefc8571107d4579…b7a3ab72d4f5ee
1 in β†’ 1 out10.2600 XPM109 B
ARzKAGFy…E5bJQ6Gf
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.

1.210 Γ— 10⁹⁴(95-digit number)
12101903508991322917…69408367001307254801
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
1.210 Γ— 10⁹⁴(95-digit number)
12101903508991322917…69408367001307254801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.420 Γ— 10⁹⁴(95-digit number)
24203807017982645835…38816734002614509601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.840 Γ— 10⁹⁴(95-digit number)
48407614035965291671…77633468005229019201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.681 Γ— 10⁹⁴(95-digit number)
96815228071930583343…55266936010458038401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.936 Γ— 10⁹⁡(96-digit number)
19363045614386116668…10533872020916076801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.872 Γ— 10⁹⁡(96-digit number)
38726091228772233337…21067744041832153601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.745 Γ— 10⁹⁡(96-digit number)
77452182457544466675…42135488083664307201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.549 Γ— 10⁹⁢(97-digit number)
15490436491508893335…84270976167328614401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.098 Γ— 10⁹⁢(97-digit number)
30980872983017786670…68541952334657228801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.196 Γ— 10⁹⁢(97-digit number)
61961745966035573340…37083904669314457601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,716,157 XPMΒ·at block #6,809,011 Β· updates every 60s
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