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Block #229,224

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/27/2013, 1:17:09 AM Β· Difficulty 9.9381 Β· 6,574,545 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a8071521e46ea16b2ae93d77ccd103c838a404457bb54ec70e9f611ffac7f562
View on Chainz β†—

Height

#229,224

Difficulty

9.938075

Transactions

1

Size

208 B

Version

2

Bits

09f025b6

Nonce

63,216

Timestamp

10/27/2013, 1:17:09 AM

Confirmations

6,574,545

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

d675c435af3c200d6e05d9e478a1f2c6b4347f0c0d6010e580ac0251f425856b
Transactions (1)
Coinbased675c435af3c20…ac0251f425856b
1 in β†’ 1 out10.1100 XPM116 B
AcLBm5Z9…S683d7c3
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.

6.488 Γ— 10⁹⁹(100-digit number)
64888742800477210577…95984744770173504001
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
6.488 Γ— 10⁹⁹(100-digit number)
64888742800477210577…95984744770173504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.297 Γ— 10¹⁰⁰(101-digit number)
12977748560095442115…91969489540347008001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.595 Γ— 10¹⁰⁰(101-digit number)
25955497120190884231…83938979080694016001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.191 Γ— 10¹⁰⁰(101-digit number)
51910994240381768462…67877958161388032001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.038 Γ— 10¹⁰¹(102-digit number)
10382198848076353692…35755916322776064001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.076 Γ— 10¹⁰¹(102-digit number)
20764397696152707384…71511832645552128001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.152 Γ— 10¹⁰¹(102-digit number)
41528795392305414769…43023665291104256001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.305 Γ— 10¹⁰¹(102-digit number)
83057590784610829539…86047330582208512001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.661 Γ— 10¹⁰²(103-digit number)
16611518156922165907…72094661164417024001
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:57,674,190 XPMΒ·at block #6,803,768 Β· updates every 60s
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