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Block #2,147,670

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/5/2017, 11:36:30 PM Β· Difficulty 10.8939 Β· 4,684,033 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
832dbdb6c7954dd24e4877c2ebb326dba8028a6100841124885d035782fd8992
View on Chainz β†—

Height

#2,147,670

Difficulty

10.893876

Transactions

2

Size

1.40 KB

Version

2

Bits

0ae4d514

Nonce

161,202,248

Timestamp

6/5/2017, 11:36:30 PM

Confirmations

4,684,033

Mined by

⛏️ P2SHAPhk81FdvvxssbpcrfuTKqLmfqaNSyh93w

Merkle Root

6dc8e700db426716a4f90e41b5b33643716fe4dd331728e599868e45659d8a91
Transactions (2)
Coinbasee8e75b27b0916d…4d6546609fe0ff
1 in β†’ 1 out8.4300 XPM110 B
APhk81Fd…aNSyh93w
3c992fccbe91f7…7cf8586a2951b2
8 in β†’ 1 out10.9747 XPM1.20 KB
AWkLrAAb…utg3dyRj
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.

2.655 Γ— 10⁹⁢(97-digit number)
26552174414856933231…87999481326221304319
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
2.655 Γ— 10⁹⁢(97-digit number)
26552174414856933231…87999481326221304319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.310 Γ— 10⁹⁢(97-digit number)
53104348829713866463…75998962652442608639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.062 Γ— 10⁹⁷(98-digit number)
10620869765942773292…51997925304885217279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.124 Γ— 10⁹⁷(98-digit number)
21241739531885546585…03995850609770434559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.248 Γ— 10⁹⁷(98-digit number)
42483479063771093170…07991701219540869119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.496 Γ— 10⁹⁷(98-digit number)
84966958127542186341…15983402439081738239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.699 Γ— 10⁹⁸(99-digit number)
16993391625508437268…31966804878163476479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.398 Γ— 10⁹⁸(99-digit number)
33986783251016874536…63933609756326952959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.797 Γ— 10⁹⁸(99-digit number)
67973566502033749073…27867219512653905919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.359 Γ— 10⁹⁹(100-digit number)
13594713300406749814…55734439025307811839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.718 Γ— 10⁹⁹(100-digit number)
27189426600813499629…11468878050615623679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,897,733 XPMΒ·at block #6,831,702 Β· updates every 60s
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