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Block #2,177,281

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/25/2017, 12:00:01 PM Β· Difficulty 10.9221 Β· 4,662,070 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6a37f2453ff859c089cdc0b42f3ff252cb7b8890f2c4e9ba86cf2c0fad76026b
View on Chainz β†—

Height

#2,177,281

Difficulty

10.922069

Transactions

2

Size

427 B

Version

2

Bits

0aec0cb5

Nonce

174,826,512

Timestamp

6/25/2017, 12:00:01 PM

Confirmations

4,662,070

Mined by

⛏️ P2SHAS37NnamsaijQMcDhZHQ7jykh9NfQXLr3Q

Merkle Root

5b106f1047fca80e3393f9514ce669a133c30f0878c6b92aa137cb3a94113706
Transactions (2)
Coinbasefe42583740ca06…5c0752dd27277a
1 in β†’ 1 out8.3800 XPM110 B
AS37Nnam…NfQXLr3Q
88e0d2f54559ad…0dd13d87763f24
1 in β†’ 2 out6776.6300 XPM226 B
Aaptx3Bu…bX7DyUNpAHNzr1C8…5ULD3YTu
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.

5.400 Γ— 10⁹⁢(97-digit number)
54006551122460140984…71273021096783359999
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
5.400 Γ— 10⁹⁢(97-digit number)
54006551122460140984…71273021096783359999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.080 Γ— 10⁹⁷(98-digit number)
10801310224492028196…42546042193566719999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.160 Γ— 10⁹⁷(98-digit number)
21602620448984056393…85092084387133439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.320 Γ— 10⁹⁷(98-digit number)
43205240897968112787…70184168774266879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.641 Γ— 10⁹⁷(98-digit number)
86410481795936225574…40368337548533759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.728 Γ— 10⁹⁸(99-digit number)
17282096359187245114…80736675097067519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.456 Γ— 10⁹⁸(99-digit number)
34564192718374490229…61473350194135039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.912 Γ— 10⁹⁸(99-digit number)
69128385436748980459…22946700388270079999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.382 Γ— 10⁹⁹(100-digit number)
13825677087349796091…45893400776540159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.765 Γ— 10⁹⁹(100-digit number)
27651354174699592183…91786801553080319999
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:57,959,094 XPMΒ·at block #6,839,350 Β· updates every 60s
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