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Block #177,937

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/24/2013, 1:16:25 AM Β· Difficulty 9.8634 Β· 6,630,363 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0d594122a6299cf65592298d3364c7daebc9bf4619f2da77a2e7b1564868eccb
View on Chainz β†—

Height

#177,937

Difficulty

9.863371

Transactions

1

Size

198 B

Version

2

Bits

09dd05df

Nonce

66,548

Timestamp

9/24/2013, 1:16:25 AM

Confirmations

6,630,363

Mined by

⛏️ P2SHAL2EWWZmctFoTxS7QgAsvUyr8tCwsD5iKb

Merkle Root

20847555634a79774080bb0beacc3f9587eccbec199bd97ebe5c7a53f6bab370
Transactions (1)
Coinbase20847555634a79…5c7a53f6bab370
1 in β†’ 1 out10.2600 XPM109 B
AL2EWWZm…CwsD5iKb
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.

9.342 Γ— 10⁹⁰(91-digit number)
93427634722566005830…52427564813349736321
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
9.342 Γ— 10⁹⁰(91-digit number)
93427634722566005830…52427564813349736321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.868 Γ— 10⁹¹(92-digit number)
18685526944513201166…04855129626699472641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.737 Γ— 10⁹¹(92-digit number)
37371053889026402332…09710259253398945281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.474 Γ— 10⁹¹(92-digit number)
74742107778052804664…19420518506797890561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.494 Γ— 10⁹²(93-digit number)
14948421555610560932…38841037013595781121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.989 Γ— 10⁹²(93-digit number)
29896843111221121865…77682074027191562241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.979 Γ— 10⁹²(93-digit number)
59793686222442243731…55364148054383124481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.195 Γ— 10⁹³(94-digit number)
11958737244488448746…10728296108766248961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.391 Γ— 10⁹³(94-digit number)
23917474488976897492…21456592217532497921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.783 Γ— 10⁹³(94-digit number)
47834948977953794985…42913184435064995841
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:57,710,453 XPMΒ·at block #6,808,299 Β· updates every 60s
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