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Block #2,880,991

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/14/2018, 5:16:07 PM Β· Difficulty 11.6296 Β· 3,958,181 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
58880d0cae859b29ca21e1b7d6b17953185fe5811c15c1253538f5beb4cec879
View on Chainz β†—

Height

#2,880,991

Difficulty

11.629574

Transactions

2

Size

4.64 KB

Version

2

Bits

0ba12bc2

Nonce

1,236,768,732

Timestamp

10/14/2018, 5:16:07 PM

Confirmations

3,958,181

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

ec86f32fe215266387a5146c0d0312c6449396cd8c8f5f73776e072ed0bc1335
Transactions (2)
Coinbasebca05fb07e0f09…e811ac3edeef62
1 in β†’ 1 out7.4300 XPM110 B
AUMQRepm…tAfKmdW1
d3857da05ae46b…8b3f6a0764c7f7
38 in β†’ 1 out1000.0000 XPM4.44 KB
AJcDB81D…ZX2on3Cs
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.

1.231 Γ— 10⁹⁡(96-digit number)
12319741525019771008…05672287535963393919
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
1.231 Γ— 10⁹⁡(96-digit number)
12319741525019771008…05672287535963393919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.463 Γ— 10⁹⁡(96-digit number)
24639483050039542016…11344575071926787839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.927 Γ— 10⁹⁡(96-digit number)
49278966100079084033…22689150143853575679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.855 Γ— 10⁹⁡(96-digit number)
98557932200158168067…45378300287707151359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.971 Γ— 10⁹⁢(97-digit number)
19711586440031633613…90756600575414302719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.942 Γ— 10⁹⁢(97-digit number)
39423172880063267227…81513201150828605439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.884 Γ— 10⁹⁢(97-digit number)
78846345760126534454…63026402301657210879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.576 Γ— 10⁹⁷(98-digit number)
15769269152025306890…26052804603314421759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.153 Γ— 10⁹⁷(98-digit number)
31538538304050613781…52105609206628843519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.307 Γ— 10⁹⁷(98-digit number)
63077076608101227563…04211218413257687039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.261 Γ— 10⁹⁸(99-digit number)
12615415321620245512…08422436826515374079
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:57,957,657 XPMΒ·at block #6,839,171 Β· updates every 60s
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