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Block #237,076

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/31/2013, 8:17:35 PM Β· Difficulty 9.9491 Β· 6,573,931 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5bd408d0db2cc493acbf4092c5c6da1e53803793defd0f5eb1f4328f7eb44708
View on Chainz β†—

Height

#237,076

Difficulty

9.949064

Transactions

1

Size

199 B

Version

2

Bits

09f2f5de

Nonce

36,697

Timestamp

10/31/2013, 8:17:35 PM

Confirmations

6,573,931

Mined by

⛏️ P2SHASeXJJsTuk2nKV74JiRd8kaBoaFfTkAVgb

Merkle Root

c40e3eee379ead873dd83696385150ee31e0db7e26ea11aed748d65a6448b1f6
Transactions (1)
Coinbasec40e3eee379ead…48d65a6448b1f6
1 in β†’ 1 out10.0900 XPM109 B
ASeXJJsT…FfTkAVgb
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.

4.970 Γ— 10⁹⁡(96-digit number)
49700881639732023734…35245857414741018801
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
4.970 Γ— 10⁹⁡(96-digit number)
49700881639732023734…35245857414741018801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.940 Γ— 10⁹⁡(96-digit number)
99401763279464047468…70491714829482037601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.988 Γ— 10⁹⁢(97-digit number)
19880352655892809493…40983429658964075201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.976 Γ— 10⁹⁢(97-digit number)
39760705311785618987…81966859317928150401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.952 Γ— 10⁹⁢(97-digit number)
79521410623571237975…63933718635856300801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.590 Γ— 10⁹⁷(98-digit number)
15904282124714247595…27867437271712601601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.180 Γ— 10⁹⁷(98-digit number)
31808564249428495190…55734874543425203201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.361 Γ— 10⁹⁷(98-digit number)
63617128498856990380…11469749086850406401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.272 Γ— 10⁹⁸(99-digit number)
12723425699771398076…22939498173700812801
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:57,732,160 XPMΒ·at block #6,811,006 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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