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Block #932,728

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/12/2015, 3:15:02 AM Β· Difficulty 10.9026 Β· 5,875,667 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
94ca67281442e2c67bc7340fa5529d95ddd9ff259c9c3ece8644ac94c15c1b62
View on Chainz β†—

Height

#932,728

Difficulty

10.902643

Transactions

2

Size

365 B

Version

2

Bits

0ae7139f

Nonce

1,107,671,249

Timestamp

2/12/2015, 3:15:02 AM

Confirmations

5,875,667

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6421e5464a67545e0a576ff1e6cd5e18c92ba6c1450c608687c2b60d92190120
Transactions (2)
Coinbasef5e05300ce7325…d4192d88d8b9c7
1 in β†’ 1 out8.4100 XPM116 B
ANSXnLY2…Sd25TjkD
b0f26484847474…d6f0c577a66eb7
1 in β†’ 1 out8.4000 XPM159 B
AekLq4Sw…ueWMfyir
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.

6.042 Γ— 10⁹⁴(95-digit number)
60426918259022992439…22805103028863277081
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
6.042 Γ— 10⁹⁴(95-digit number)
60426918259022992439…22805103028863277081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.208 Γ— 10⁹⁡(96-digit number)
12085383651804598487…45610206057726554161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.417 Γ— 10⁹⁡(96-digit number)
24170767303609196975…91220412115453108321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.834 Γ— 10⁹⁡(96-digit number)
48341534607218393951…82440824230906216641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.668 Γ— 10⁹⁡(96-digit number)
96683069214436787903…64881648461812433281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.933 Γ— 10⁹⁢(97-digit number)
19336613842887357580…29763296923624866561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.867 Γ— 10⁹⁢(97-digit number)
38673227685774715161…59526593847249733121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.734 Γ— 10⁹⁢(97-digit number)
77346455371549430322…19053187694499466241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.546 Γ— 10⁹⁷(98-digit number)
15469291074309886064…38106375388998932481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.093 Γ— 10⁹⁷(98-digit number)
30938582148619772129…76212750777997864961
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:57,711,216 XPMΒ·at block #6,808,394 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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