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Block #157,836

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2013, 9:56:06 PM Β· Difficulty 9.8692 Β· 6,651,997 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7850e5ec897d21c6fce10e08838bec2104ba67696322df7008c1914d3e283e4f
View on Chainz β†—

Height

#157,836

Difficulty

9.869187

Transactions

1

Size

199 B

Version

2

Bits

09de830a

Nonce

97,405

Timestamp

9/9/2013, 9:56:06 PM

Confirmations

6,651,997

Mined by

⛏️ P2SHAQwvDA69KmKhGQHW3Z8SBjRvog5ujbnyih

Merkle Root

e945540f1aa68124f56821a24748a97cc30304377e513b31327c8dc8931e970f
Transactions (1)
Coinbasee945540f1aa681…7c8dc8931e970f
1 in β†’ 1 out10.2500 XPM109 B
AQwvDA69…5ujbnyih
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.

1.234 Γ— 10⁹⁡(96-digit number)
12346709321471206662…83661739226534336001
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
1.234 Γ— 10⁹⁡(96-digit number)
12346709321471206662…83661739226534336001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.469 Γ— 10⁹⁡(96-digit number)
24693418642942413324…67323478453068672001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.938 Γ— 10⁹⁡(96-digit number)
49386837285884826649…34646956906137344001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.877 Γ— 10⁹⁡(96-digit number)
98773674571769653299…69293913812274688001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.975 Γ— 10⁹⁢(97-digit number)
19754734914353930659…38587827624549376001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.950 Γ— 10⁹⁢(97-digit number)
39509469828707861319…77175655249098752001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.901 Γ— 10⁹⁢(97-digit number)
79018939657415722639…54351310498197504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.580 Γ— 10⁹⁷(98-digit number)
15803787931483144527…08702620996395008001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.160 Γ— 10⁹⁷(98-digit number)
31607575862966289055…17405241992790016001
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:57,722,750 XPMΒ·at block #6,809,832 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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