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Block #2,099,991

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2017, 9:41:26 PM Β· Difficulty 10.8554 Β· 4,726,120 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3d57b9ba5594eb472d67c06a34d41983450f37785447dd73c03b47286db5c9d2
View on Chainz β†—

Height

#2,099,991

Difficulty

10.855440

Transactions

2

Size

14.83 KB

Version

2

Bits

0adafe21

Nonce

503,044,913

Timestamp

5/4/2017, 9:41:26 PM

Confirmations

4,726,120

Mined by

⛏️ P2SHAWysn8W7ktcJYG8ciazX1GssCD1D3qDPcq

Merkle Root

167bce4f7a7df95c1aee2f54dcb66358fbdd5baf054fe8889599ecdd39330b0c
Transactions (2)
Coinbaseef81d0888b18c0…5f83c5155483b4
1 in β†’ 1 out9.1300 XPM109 B
AWysn8W7…1D3qDPcq
c268640dd491a3…32d5668c883d0a
101 in β†’ 1 out1540.6006 XPM14.63 KB
AMRycWoF…13hkF5ou
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.

1.428 Γ— 10⁹⁡(96-digit number)
14288411027822440443…61956448630889832799
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
1.428 Γ— 10⁹⁡(96-digit number)
14288411027822440443…61956448630889832799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.857 Γ— 10⁹⁡(96-digit number)
28576822055644880887…23912897261779665599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.715 Γ— 10⁹⁡(96-digit number)
57153644111289761774…47825794523559331199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.143 Γ— 10⁹⁢(97-digit number)
11430728822257952354…95651589047118662399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.286 Γ— 10⁹⁢(97-digit number)
22861457644515904709…91303178094237324799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.572 Γ— 10⁹⁢(97-digit number)
45722915289031809419…82606356188474649599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.144 Γ— 10⁹⁢(97-digit number)
91445830578063618838…65212712376949299199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.828 Γ— 10⁹⁷(98-digit number)
18289166115612723767…30425424753898598399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.657 Γ— 10⁹⁷(98-digit number)
36578332231225447535…60850849507797196799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.315 Γ— 10⁹⁷(98-digit number)
73156664462450895071…21701699015594393599
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:57,853,012 XPMΒ·at block #6,826,110 Β· updates every 60s
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