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Block #154,123

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/7/2013, 11:18:36 AM Β· Difficulty 9.8639 Β· 6,649,627 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
37310ee302b45c0b59eada778c50e0c640713c18275c957569705b0c603b76e4
View on Chainz β†—

Height

#154,123

Difficulty

9.863924

Transactions

2

Size

425 B

Version

2

Bits

09dd2a18

Nonce

116,724

Timestamp

9/7/2013, 11:18:36 AM

Confirmations

6,649,627

Mined by

⛏️ P2SHASavm3ME46ZqiTbhj6XSFZmH8ooKTKKkrn

Merkle Root

7e6c9fcf51035c7bb951684eebcad0f5a9494baa3bb45195804bb75a3587adaf
Transactions (2)
Coinbaseacc1ff5b2892f0…20c2b7e284a190
1 in β†’ 1 out10.2700 XPM109 B
ASavm3ME…oKTKKkrn
f9e0f350656a93…808205fc3b5f85
1 in β†’ 2 out2.1069 XPM226 B
AJqoRC1a…2g8pjMwuAcN7Mwej…Rnr1man2
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.

1.046 Γ— 10⁹⁡(96-digit number)
10461429352647798360…94210719918481003201
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
1.046 Γ— 10⁹⁡(96-digit number)
10461429352647798360…94210719918481003201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.092 Γ— 10⁹⁡(96-digit number)
20922858705295596720…88421439836962006401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.184 Γ— 10⁹⁡(96-digit number)
41845717410591193440…76842879673924012801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.369 Γ— 10⁹⁡(96-digit number)
83691434821182386881…53685759347848025601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.673 Γ— 10⁹⁢(97-digit number)
16738286964236477376…07371518695696051201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.347 Γ— 10⁹⁢(97-digit number)
33476573928472954752…14743037391392102401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.695 Γ— 10⁹⁢(97-digit number)
66953147856945909505…29486074782784204801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.339 Γ— 10⁹⁷(98-digit number)
13390629571389181901…58972149565568409601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.678 Γ— 10⁹⁷(98-digit number)
26781259142778363802…17944299131136819201
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:57,674,039 XPMΒ·at block #6,803,749 Β· updates every 60s
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