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Block #163,887

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/14/2013, 7:41:37 AM Β· Difficulty 9.8616 Β· 6,644,245 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
62b3dce98beba3e3e53af3a7dfa02a4d8e8b752abb231d4f835d4bde922f9e04
View on Chainz β†—

Height

#163,887

Difficulty

9.861578

Transactions

1

Size

197 B

Version

2

Bits

09dc9067

Nonce

65,596

Timestamp

9/14/2013, 7:41:37 AM

Confirmations

6,644,245

Mined by

⛏️ P2SHARBvr1evuYzdjmXQBMTxCmA4hCNg7YPkPH

Merkle Root

e123a7d8cab9228313158d1d2a0943f266b8b7482d8814a9ba260a67910b8017
Transactions (1)
Coinbasee123a7d8cab922…260a67910b8017
1 in β†’ 1 out10.2700 XPM109 B
ARBvr1ev…Ng7YPkPH
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.

5.194 Γ— 10⁹⁰(91-digit number)
51943458925747408008…42717762892679134081
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
5.194 Γ— 10⁹⁰(91-digit number)
51943458925747408008…42717762892679134081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.038 Γ— 10⁹¹(92-digit number)
10388691785149481601…85435525785358268161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.077 Γ— 10⁹¹(92-digit number)
20777383570298963203…70871051570716536321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.155 Γ— 10⁹¹(92-digit number)
41554767140597926406…41742103141433072641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.310 Γ— 10⁹¹(92-digit number)
83109534281195852813…83484206282866145281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.662 Γ— 10⁹²(93-digit number)
16621906856239170562…66968412565732290561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.324 Γ— 10⁹²(93-digit number)
33243813712478341125…33936825131464581121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.648 Γ— 10⁹²(93-digit number)
66487627424956682250…67873650262929162241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.329 Γ— 10⁹³(94-digit number)
13297525484991336450…35747300525858324481
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:57,709,097 XPMΒ·at block #6,808,131 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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