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Block #149,180

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/4/2013, 5:19:19 AM Β· Difficulty 9.8565 Β· 6,657,947 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0c8edb5400976f015a764e9e9cc2392d6a7ee6cf3a7eb03537ce7d51b5fea4b7
View on Chainz β†—

Height

#149,180

Difficulty

9.856455

Transactions

1

Size

198 B

Version

2

Bits

09db40a7

Nonce

594,998

Timestamp

9/4/2013, 5:19:19 AM

Confirmations

6,657,947

Mined by

⛏️ P2SHAJkcBGvuouoWiEQ4AmFvGo3qwPhSNwhPED

Merkle Root

6aad0d83c63d618c77da80189d7f129e06e9fdd783790b2dbe83e84eb0fc2eb0
Transactions (1)
Coinbase6aad0d83c63d61…83e84eb0fc2eb0
1 in β†’ 1 out10.2800 XPM109 B
AJkcBGvu…hSNwhPED
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.

1.006 Γ— 10⁹²(93-digit number)
10063918406762308001…66070614682652985601
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
1.006 Γ— 10⁹²(93-digit number)
10063918406762308001…66070614682652985601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.012 Γ— 10⁹²(93-digit number)
20127836813524616003…32141229365305971201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.025 Γ— 10⁹²(93-digit number)
40255673627049232007…64282458730611942401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.051 Γ— 10⁹²(93-digit number)
80511347254098464014…28564917461223884801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.610 Γ— 10⁹³(94-digit number)
16102269450819692802…57129834922447769601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.220 Γ— 10⁹³(94-digit number)
32204538901639385605…14259669844895539201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.440 Γ— 10⁹³(94-digit number)
64409077803278771211…28519339689791078401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.288 Γ— 10⁹⁴(95-digit number)
12881815560655754242…57038679379582156801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.576 Γ— 10⁹⁴(95-digit number)
25763631121311508484…14077358759164313601
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:57,701,120 XPMΒ·at block #6,807,126 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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