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Block #693,170

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/26/2014, 3:18:56 AM Β· Difficulty 10.9563 Β· 6,113,668 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a81a254c263293ac2d66bd9711107b064fd23b83cf75e4060f3f26395bcea52f
View on Chainz β†—

Height

#693,170

Difficulty

10.956322

Transactions

2

Size

1.92 KB

Version

2

Bits

0af4d180

Nonce

360,699,329

Timestamp

8/26/2014, 3:18:56 AM

Confirmations

6,113,668

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c65f62667644d1842d22dc3a7063e870d5bff0afa75463aa5655afb5a8c11c9b
Transactions (2)
Coinbase31c76119b35707…daf1ba7a0c3648
1 in β†’ 1 out8.3400 XPM116 B
ANSXnLY2…Sd25TjkD
3db4375e6c7a5b…491b2b5494e784
15 in β†’ 1 out153.9500 XPM1.72 KB
AMWKfUWU…hjT6U8ko
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.

9.727 Γ— 10⁹⁴(95-digit number)
97277290629893334529…09055731873567244801
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
9.727 Γ— 10⁹⁴(95-digit number)
97277290629893334529…09055731873567244801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.945 Γ— 10⁹⁡(96-digit number)
19455458125978666905…18111463747134489601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.891 Γ— 10⁹⁡(96-digit number)
38910916251957333811…36222927494268979201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.782 Γ— 10⁹⁡(96-digit number)
77821832503914667623…72445854988537958401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.556 Γ— 10⁹⁢(97-digit number)
15564366500782933524…44891709977075916801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.112 Γ— 10⁹⁢(97-digit number)
31128733001565867049…89783419954151833601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.225 Γ— 10⁹⁢(97-digit number)
62257466003131734098…79566839908303667201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.245 Γ— 10⁹⁷(98-digit number)
12451493200626346819…59133679816607334401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.490 Γ— 10⁹⁷(98-digit number)
24902986401252693639…18267359633214668801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.980 Γ— 10⁹⁷(98-digit number)
49805972802505387278…36534719266429337601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.961 Γ— 10⁹⁷(98-digit number)
99611945605010774557…73069438532858675201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,698,807 XPMΒ·at block #6,806,837 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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