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Block #1,393,494

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/31/2015, 8:18:43 PM Β· Difficulty 10.8100 Β· 5,415,540 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aad04bc541522b0aae8df973aa3537838557ccb0d51d2e8c119a25e7a47e377b
View on Chainz β†—

Height

#1,393,494

Difficulty

10.810019

Transactions

2

Size

3.02 KB

Version

2

Bits

0acf5d6e

Nonce

412,913,989

Timestamp

12/31/2015, 8:18:43 PM

Confirmations

5,415,540

Mined by

⛏️ P2SHAb8Q4kX9AgQFXHQzobX4qG5dup53GNQhon

Merkle Root

3ed96b5fc01ca7eadf1c1097ac65f08f92097b41ffc244d600e4a76c8faff70d
Transactions (2)
Coinbase503ed28bc9d3ca…bfec3216cd6003
1 in β†’ 1 out8.5700 XPM110 B
Ab8Q4kX9…53GNQhon
5eae3d981072c9…6fd5216c3f07e1
19 in β†’ 2 out74.6251 XPM2.82 KB
ASZR8uSi…DjzSZVoEAcMpew3F…1yR4JhRa
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.

5.384 Γ— 10⁹⁡(96-digit number)
53842360722595503977…39264131076814023679
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
5.384 Γ— 10⁹⁡(96-digit number)
53842360722595503977…39264131076814023679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.076 Γ— 10⁹⁢(97-digit number)
10768472144519100795…78528262153628047359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.153 Γ— 10⁹⁢(97-digit number)
21536944289038201591…57056524307256094719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.307 Γ— 10⁹⁢(97-digit number)
43073888578076403182…14113048614512189439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.614 Γ— 10⁹⁢(97-digit number)
86147777156152806364…28226097229024378879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.722 Γ— 10⁹⁷(98-digit number)
17229555431230561272…56452194458048757759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.445 Γ— 10⁹⁷(98-digit number)
34459110862461122545…12904388916097515519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.891 Γ— 10⁹⁷(98-digit number)
68918221724922245091…25808777832195031039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.378 Γ— 10⁹⁸(99-digit number)
13783644344984449018…51617555664390062079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.756 Γ— 10⁹⁸(99-digit number)
27567288689968898036…03235111328780124159
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:57,716,337 XPMΒ·at block #6,809,033 Β· updates every 60s
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