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Block #919,497

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/2/2015, 5:41:31 AM Β· Difficulty 10.9202 Β· 5,889,957 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3cb9178a372fc6b95c30a4a48f78f25f2bbe96079cad041f46a8fe09501f0b57
View on Chainz β†—

Height

#919,497

Difficulty

10.920171

Transactions

2

Size

1.58 KB

Version

2

Bits

0aeb905b

Nonce

156,197,320

Timestamp

2/2/2015, 5:41:31 AM

Confirmations

5,889,957

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

66af8afc10d96723aab9e7812d5903e02fd14e969ce15368e257e784ddba4fb8
Transactions (2)
Coinbase7fb0f7028f9714…4512d51546ccf9
1 in β†’ 1 out8.3900 XPM116 B
ANSXnLY2…Sd25TjkD
37dab8a6918d12…f162564facd4ce
9 in β†’ 2 out349.8499 XPM1.38 KB
AUVhbPyt…PJiV3oAFAQ5fy2sY…PEW6voxh
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.

4.375 Γ— 10⁹⁴(95-digit number)
43756973606906808099…93325352665696350059
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.375 Γ— 10⁹⁴(95-digit number)
43756973606906808099…93325352665696350059
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.751 Γ— 10⁹⁴(95-digit number)
87513947213813616198…86650705331392700119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.750 Γ— 10⁹⁡(96-digit number)
17502789442762723239…73301410662785400239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.500 Γ— 10⁹⁡(96-digit number)
35005578885525446479…46602821325570800479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.001 Γ— 10⁹⁡(96-digit number)
70011157771050892959…93205642651141600959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.400 Γ— 10⁹⁢(97-digit number)
14002231554210178591…86411285302283201919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.800 Γ— 10⁹⁢(97-digit number)
28004463108420357183…72822570604566403839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.600 Γ— 10⁹⁢(97-digit number)
56008926216840714367…45645141209132807679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.120 Γ— 10⁹⁷(98-digit number)
11201785243368142873…91290282418265615359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.240 Γ— 10⁹⁷(98-digit number)
22403570486736285746…82580564836531230719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.480 Γ— 10⁹⁷(98-digit number)
44807140973472571493…65161129673062461439
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,719,703 XPMΒ·at block #6,809,453 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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