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Block #923,477

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/5/2015, 7:04:49 AM Β· Difficulty 10.9133 Β· 5,872,185 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
846d2093ad6afbbba323c3eb80b1cadc7dfdaee0e9fc0dac103de0d3929357d6
View on Chainz β†—

Height

#923,477

Difficulty

10.913307

Transactions

2

Size

1.15 KB

Version

2

Bits

0ae9ce83

Nonce

467,714,482

Timestamp

2/5/2015, 7:04:49 AM

Confirmations

5,872,185

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b7c03f3e554c7598fcb2d5e2b481214504ea24be85600661f1179a98e831360a
Transactions (2)
Coinbase0cc340ff7e4c78…805fd1ddd3e99c
1 in β†’ 1 out8.4000 XPM116 B
ANSXnLY2…Sd25TjkD
515e60422684eb…2dc13c23528006
6 in β†’ 2 out1461.0000 XPM967 B
AG6g15Lu…okSG4T9kAQQxUbQj…byBCB7iu
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.

1.026 Γ— 10⁹⁡(96-digit number)
10260283772907759111…40674567277654881599
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
1.026 Γ— 10⁹⁡(96-digit number)
10260283772907759111…40674567277654881599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.052 Γ— 10⁹⁡(96-digit number)
20520567545815518222…81349134555309763199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.104 Γ— 10⁹⁡(96-digit number)
41041135091631036444…62698269110619526399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.208 Γ— 10⁹⁡(96-digit number)
82082270183262072888…25396538221239052799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.641 Γ— 10⁹⁢(97-digit number)
16416454036652414577…50793076442478105599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.283 Γ— 10⁹⁢(97-digit number)
32832908073304829155…01586152884956211199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.566 Γ— 10⁹⁢(97-digit number)
65665816146609658310…03172305769912422399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.313 Γ— 10⁹⁷(98-digit number)
13133163229321931662…06344611539824844799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.626 Γ— 10⁹⁷(98-digit number)
26266326458643863324…12689223079649689599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.253 Γ— 10⁹⁷(98-digit number)
52532652917287726648…25378446159299379199
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,609,368 XPMΒ·at block #6,795,661 Β· updates every 60s
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