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Block #2,099,341

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2017, 10:03:57 AM Β· Difficulty 10.8568 Β· 4,727,607 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7a562acee6bfce03e462a7f00dfcea68646b75236f813700f26e0e8d39b74d7b
View on Chainz β†—

Height

#2,099,341

Difficulty

10.856752

Transactions

2

Size

13.69 KB

Version

2

Bits

0adb5412

Nonce

792,148,795

Timestamp

5/4/2017, 10:03:57 AM

Confirmations

4,727,607

Mined by

⛏️ P2SHAJa5QRxkGKUHN4GGzwsTbE7mqdeg6uV37M

Merkle Root

6a955125d4282b3983cd8939072494f8126c58a8920c9b5209e206b5e9cea7a8
Transactions (2)
Coinbasec251fbb2efc441…6ca72ef9118feb
1 in β†’ 1 out8.7200 XPM109 B
AJa5QRxk…eg6uV37M
4cd11b7c2adf7f…25da476be243b2
93 in β†’ 1 out4.9990 XPM13.49 KB
AUjBeKZH…3MTP1SQk
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.

5.810 Γ— 10⁹⁴(95-digit number)
58100321196376753279…71755839619099199039
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
5.810 Γ— 10⁹⁴(95-digit number)
58100321196376753279…71755839619099199039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.162 Γ— 10⁹⁡(96-digit number)
11620064239275350655…43511679238198398079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.324 Γ— 10⁹⁡(96-digit number)
23240128478550701311…87023358476396796159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.648 Γ— 10⁹⁡(96-digit number)
46480256957101402623…74046716952793592319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.296 Γ— 10⁹⁡(96-digit number)
92960513914202805247…48093433905587184639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.859 Γ— 10⁹⁢(97-digit number)
18592102782840561049…96186867811174369279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.718 Γ— 10⁹⁢(97-digit number)
37184205565681122099…92373735622348738559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.436 Γ— 10⁹⁢(97-digit number)
74368411131362244198…84747471244697477119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.487 Γ— 10⁹⁷(98-digit number)
14873682226272448839…69494942489394954239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.974 Γ— 10⁹⁷(98-digit number)
29747364452544897679…38989884978789908479
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:57,859,759 XPMΒ·at block #6,826,947 Β· updates every 60s
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