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Block #3,146,410

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 4/19/2019, 3:36:00 PM Β· Difficulty 11.3234 Β· 3,692,634 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0cba0ab8ed45c9e19ebcc9348539968389e60d29d56854d3f5d90ae716de80af
View on Chainz β†—

Height

#3,146,410

Difficulty

11.323381

Transactions

2

Size

575 B

Version

2

Bits

0b52c919

Nonce

213,542,824

Timestamp

4/19/2019, 3:36:00 PM

Confirmations

3,692,634

Mined by

⛏️ P2SHARbm48qRsZyALB7gqdgsMMKGGA9xQc8DBX

Merkle Root

9e006f87ed135e822266f833e01b56aa90b846daa74812369b1f238db2fb070c
Transactions (2)
Coinbase2b221a3a323884…9d39a758831c79
1 in β†’ 1 out7.8000 XPM110 B
ARbm48qR…9xQc8DBX
783e5c7ff41f6f…c30a248de8a65e
2 in β†’ 2 out590.3219 XPM374 B
AeTHTL7A…vT1872bkAJRnWa3c…rinYBg8w
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.

3.465 Γ— 10⁹⁢(97-digit number)
34653119044862899553…64542420966516981759
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
3.465 Γ— 10⁹⁢(97-digit number)
34653119044862899553…64542420966516981759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.930 Γ— 10⁹⁢(97-digit number)
69306238089725799106…29084841933033963519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.386 Γ— 10⁹⁷(98-digit number)
13861247617945159821…58169683866067927039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.772 Γ— 10⁹⁷(98-digit number)
27722495235890319642…16339367732135854079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.544 Γ— 10⁹⁷(98-digit number)
55444990471780639284…32678735464271708159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.108 Γ— 10⁹⁸(99-digit number)
11088998094356127856…65357470928543416319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.217 Γ— 10⁹⁸(99-digit number)
22177996188712255713…30714941857086832639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.435 Γ— 10⁹⁸(99-digit number)
44355992377424511427…61429883714173665279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.871 Γ— 10⁹⁸(99-digit number)
88711984754849022855…22859767428347330559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.774 Γ— 10⁹⁹(100-digit number)
17742396950969804571…45719534856694661119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.548 Γ— 10⁹⁹(100-digit number)
35484793901939609142…91439069713389322239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
7.096 Γ— 10⁹⁹(100-digit number)
70969587803879218284…82878139426778644479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,956,621 XPMΒ·at block #6,839,043 Β· updates every 60s
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