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Block #2,127,156

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/21/2017, 6:50:02 PM Β· Difficulty 10.9187 Β· 4,714,592 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d46c4bd922797ec5803c0ec50edca8b0a43026f5770a2ea0de692f8c7ef64a39
View on Chainz β†—

Height

#2,127,156

Difficulty

10.918655

Transactions

1

Size

242 B

Version

2

Bits

0aeb2d01

Nonce

468,074,488

Timestamp

5/21/2017, 6:50:02 PM

Confirmations

4,714,592

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

7549caacf891eb377ba9cc2323298ef6ddd9fcee18164797f20464ecf4a73380
Transactions (1)
Coinbase7549caacf891eb…0464ecf4a73380
1 in β†’ 2 out8.3700 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

3.103 Γ— 10⁹⁴(95-digit number)
31032723001511955978…08833139201224245219
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
3.103 Γ— 10⁹⁴(95-digit number)
31032723001511955978…08833139201224245219
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.206 Γ— 10⁹⁴(95-digit number)
62065446003023911956…17666278402448490439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.241 Γ— 10⁹⁡(96-digit number)
12413089200604782391…35332556804896980879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.482 Γ— 10⁹⁡(96-digit number)
24826178401209564782…70665113609793961759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.965 Γ— 10⁹⁡(96-digit number)
49652356802419129565…41330227219587923519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.930 Γ— 10⁹⁡(96-digit number)
99304713604838259130…82660454439175847039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.986 Γ— 10⁹⁢(97-digit number)
19860942720967651826…65320908878351694079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.972 Γ— 10⁹⁢(97-digit number)
39721885441935303652…30641817756703388159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.944 Γ— 10⁹⁢(97-digit number)
79443770883870607304…61283635513406776319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.588 Γ— 10⁹⁷(98-digit number)
15888754176774121460…22567271026813552639
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:57,978,369 XPMΒ·at block #6,841,747 Β· updates every 60s
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