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Block #149,014

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/4/2013, 2:21:22 AM Β· Difficulty 9.8567 Β· 6,667,074 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
55cd753582ed97576ea300d643a36b2afa458bbbc7e202e4a7f8b80a97e5c53e
View on Chainz β†—

Height

#149,014

Difficulty

9.856694

Transactions

1

Size

202 B

Version

2

Bits

09db504c

Nonce

526,966

Timestamp

9/4/2013, 2:21:22 AM

Confirmations

6,667,074

Mined by

⛏️ P2SHAT5A2KL6kAm5Pa3anhC8W4LVscCT16n6i2

Merkle Root

233981b2b30ce3c803c051c5caf2f5e15b31befbb383df6e28a72a2bfcd9890b
Transactions (1)
Coinbase233981b2b30ce3…a72a2bfcd9890b
1 in β†’ 1 out10.2800 XPM112 B
AT5A2KL6…CT16n6i2
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.

1.054 Γ— 10⁹⁡(96-digit number)
10544507018400372312…62238414208924856361
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
1.054 Γ— 10⁹⁡(96-digit number)
10544507018400372312…62238414208924856361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.108 Γ— 10⁹⁡(96-digit number)
21089014036800744625…24476828417849712721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.217 Γ— 10⁹⁡(96-digit number)
42178028073601489251…48953656835699425441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.435 Γ— 10⁹⁡(96-digit number)
84356056147202978502…97907313671398850881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.687 Γ— 10⁹⁢(97-digit number)
16871211229440595700…95814627342797701761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.374 Γ— 10⁹⁢(97-digit number)
33742422458881191401…91629254685595403521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.748 Γ— 10⁹⁢(97-digit number)
67484844917762382802…83258509371190807041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.349 Γ— 10⁹⁷(98-digit number)
13496968983552476560…66517018742381614081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.699 Γ— 10⁹⁷(98-digit number)
26993937967104953120…33034037484763228161
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:57,772,823 XPMΒ·at block #6,816,087 Β· updates every 60s
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