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Block #643,093

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/22/2014, 4:23:55 AM Β· Difficulty 10.9569 Β· 6,163,790 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
acd8bfc44cfcfddb71e2f1cfc18ca88ddf9a540becac79c4a32e8228dc33ae02
View on Chainz β†—

Height

#643,093

Difficulty

10.956882

Transactions

2

Size

581 B

Version

2

Bits

0af4f637

Nonce

3,150,629,961

Timestamp

7/22/2014, 4:23:55 AM

Confirmations

6,163,790

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e6047bde89fea45c221d01d968ab58efdf6a2a52f932c0ae1c99e504fd52f242
Transactions (2)
Coinbase41eb1558e178a7…6f59c7c79bd071
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
2bf995ca51a8a8…581fa8c6c7c7e2
2 in β†’ 2 out10.6429 XPM374 B
AXC8EZRC…KxnGmkGDAc6nng4Z…X3Jy48Wq
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.

2.486 Γ— 10⁹⁷(98-digit number)
24866075092748743283…64681891201283901441
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
2.486 Γ— 10⁹⁷(98-digit number)
24866075092748743283…64681891201283901441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.973 Γ— 10⁹⁷(98-digit number)
49732150185497486567…29363782402567802881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.946 Γ— 10⁹⁷(98-digit number)
99464300370994973134…58727564805135605761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.989 Γ— 10⁹⁸(99-digit number)
19892860074198994626…17455129610271211521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.978 Γ— 10⁹⁸(99-digit number)
39785720148397989253…34910259220542423041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.957 Γ— 10⁹⁸(99-digit number)
79571440296795978507…69820518441084846081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.591 Γ— 10⁹⁹(100-digit number)
15914288059359195701…39641036882169692161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.182 Γ— 10⁹⁹(100-digit number)
31828576118718391403…79282073764339384321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.365 Γ— 10⁹⁹(100-digit number)
63657152237436782806…58564147528678768641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.273 Γ— 10¹⁰⁰(101-digit number)
12731430447487356561…17128295057357537281
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,699,173 XPMΒ·at block #6,806,882 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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