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Block #63,538

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2013, 2:07:06 AM Β· Difficulty 8.9794 Β· 6,744,738 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ab97bc4d52acd0c6eb1d4e5637573a1bf51fce87a9ed99f383e0e79c94a4b3c4
View on Chainz β†—

Height

#63,538

Difficulty

8.979427

Transactions

2

Size

723 B

Version

2

Bits

08fabbb4

Nonce

104

Timestamp

7/19/2013, 2:07:06 AM

Confirmations

6,744,738

Mined by

⛏️ P2SHAMQ5wtVBEQrAYJzGcvop4fLNJu1fk2PgqH

Merkle Root

24c1196c02296ff09ec577f0973d31afde631e1813c3169f4780b024bcd28522
Transactions (2)
Coinbase336312a8b032c9…20ca9bb4d34477
1 in β†’ 1 out12.3900 XPM109 B
AMQ5wtVB…1fk2PgqH
0cbf790a46aa77…321a6a44c4cabf
3 in β†’ 2 out99.9171 XPM523 B
AW7aqm7z…MZ7TogRxAPzCRdkA…sSL2k2Tz
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.

2.247 Γ— 10⁹⁷(98-digit number)
22471740958648511443…11178354237473830311
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
2.247 Γ— 10⁹⁷(98-digit number)
22471740958648511443…11178354237473830311
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.494 Γ— 10⁹⁷(98-digit number)
44943481917297022887…22356708474947660621
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.988 Γ— 10⁹⁷(98-digit number)
89886963834594045774…44713416949895321241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.797 Γ— 10⁹⁸(99-digit number)
17977392766918809154…89426833899790642481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.595 Γ— 10⁹⁸(99-digit number)
35954785533837618309…78853667799581284961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.190 Γ— 10⁹⁸(99-digit number)
71909571067675236619…57707335599162569921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.438 Γ— 10⁹⁹(100-digit number)
14381914213535047323…15414671198325139841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.876 Γ— 10⁹⁹(100-digit number)
28763828427070094647…30829342396650279681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.752 Γ— 10⁹⁹(100-digit number)
57527656854140189295…61658684793300559361
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:57,710,258 XPMΒ·at block #6,808,275 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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