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Block #195,451

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/5/2013, 7:44:45 PM Β· Difficulty 9.8804 Β· 6,620,856 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
98c2cb01e6944c96f2ce6ba0ab402fc685b8c1738988a272c1cb929032a9d7ca
View on Chainz β†—

Height

#195,451

Difficulty

9.880353

Transactions

3

Size

651 B

Version

2

Bits

09e15ec9

Nonce

106,179

Timestamp

10/5/2013, 7:44:45 PM

Confirmations

6,620,856

Mined by

⛏️ P2SHAJYjKv6MiC978JMgPHsTyLZP4H8TXfzr5c

Merkle Root

d863823705d5cdffc81a3d55f4b929d6483c766069f3b3ef2a58881e0c9a530b
Transactions (3)
Coinbase2ed186e17ea686…d4cab1234bf835
1 in β†’ 1 out10.2500 XPM109 B
AJYjKv6M…8TXfzr5c
84ad97174e5e24…1398cd56be8358
1 in β†’ 2 out10.2300 XPM225 B
AN3QK9wE…SHQv3wVgAYvza539…GJ1XJfZX
842c84d766e322…a911c96c2fa037
1 in β†’ 2 out10.2300 XPM227 B
AdWp2YRv…FDtt217aAcht4ti5…5UiSZ17b
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.

2.389 Γ— 10⁹⁴(95-digit number)
23891012823333341931…89735146255288796401
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
2.389 Γ— 10⁹⁴(95-digit number)
23891012823333341931…89735146255288796401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.778 Γ— 10⁹⁴(95-digit number)
47782025646666683862…79470292510577592801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.556 Γ— 10⁹⁴(95-digit number)
95564051293333367724…58940585021155185601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.911 Γ— 10⁹⁡(96-digit number)
19112810258666673544…17881170042310371201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.822 Γ— 10⁹⁡(96-digit number)
38225620517333347089…35762340084620742401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.645 Γ— 10⁹⁡(96-digit number)
76451241034666694179…71524680169241484801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.529 Γ— 10⁹⁢(97-digit number)
15290248206933338835…43049360338482969601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.058 Γ— 10⁹⁢(97-digit number)
30580496413866677671…86098720676965939201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.116 Γ— 10⁹⁢(97-digit number)
61160992827733355343…72197441353931878401
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:57,774,576 XPMΒ·at block #6,816,306 Β· updates every 60s
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