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Block #245,547

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/5/2013, 1:05:30 PM Β· Difficulty 9.9640 Β· 6,550,176 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eb5a8b42f876bcf83be8ac909f9873bebdfe81f5a9a8c21153a114d86c09ac89
View on Chainz β†—

Height

#245,547

Difficulty

9.963974

Transactions

2

Size

1.43 KB

Version

2

Bits

09f6c706

Nonce

23,618

Timestamp

11/5/2013, 1:05:30 PM

Confirmations

6,550,176

Mined by

⛏️ P2SHAQmuF7GjzREjvYSApiMxaVd2u4x6a9WFvi

Merkle Root

332ec7f0f0114b2bff4996061c1e21e62e62b39fac7c0be3b8d6940f70314a5f
Transactions (2)
Coinbase9b4e4b8e53b0a2…9d21982e32fb95
1 in β†’ 1 out10.0800 XPM109 B
AQmuF7Gj…x6a9WFvi
f886170894ce07…2ad92cb3d6b82a
8 in β†’ 2 out50.1004 XPM1.23 KB
ALADBzoA…UX3rRXrSAZEs1KdH…ApJqK4ag
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.

2.836 Γ— 10⁹⁡(96-digit number)
28368014746731396247…95012755259515801601
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
2.836 Γ— 10⁹⁡(96-digit number)
28368014746731396247…95012755259515801601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.673 Γ— 10⁹⁡(96-digit number)
56736029493462792495…90025510519031603201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.134 Γ— 10⁹⁢(97-digit number)
11347205898692558499…80051021038063206401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.269 Γ— 10⁹⁢(97-digit number)
22694411797385116998…60102042076126412801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.538 Γ— 10⁹⁢(97-digit number)
45388823594770233996…20204084152252825601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.077 Γ— 10⁹⁢(97-digit number)
90777647189540467992…40408168304505651201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.815 Γ— 10⁹⁷(98-digit number)
18155529437908093598…80816336609011302401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.631 Γ— 10⁹⁷(98-digit number)
36311058875816187197…61632673218022604801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.262 Γ— 10⁹⁷(98-digit number)
72622117751632374394…23265346436045209601
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:57,609,859 XPMΒ·at block #6,795,722 Β· updates every 60s
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