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Block #1,486,407

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/6/2016, 4:55:15 PM Β· Difficulty 10.7258 Β· 5,321,642 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
104e7768e2164a5d11501de43077460f91ed924b34201901c0cdb966557fb0ff
View on Chainz β†—

Height

#1,486,407

Difficulty

10.725790

Transactions

2

Size

69.04 KB

Version

2

Bits

0ab9cd5e

Nonce

205,225,127

Timestamp

3/6/2016, 4:55:15 PM

Confirmations

5,321,642

Mined by

⛏️ P2SHAe9aiyr4XK4uPd17qJEZVD6A88CLGh79ym

Merkle Root

da6e00ed0352ebcf19450a6c2793ec091e3fd5dd193c9bbef6de0c1784015e35
Transactions (2)
Coinbase6aa3f14e3b8fff…b35ec67f56240d
1 in β†’ 1 out9.3900 XPM110 B
Ae9aiyr4…CLGh79ym
6cc4347f28e6ec…73b5b4615fcc90
618 in β†’ 1 out5375.0765 XPM68.84 KB
ARdVe6hk…QmgEA7NV
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.

9.764 Γ— 10⁹⁢(97-digit number)
97649474811548259980…14421399877292881921
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
9.764 Γ— 10⁹⁢(97-digit number)
97649474811548259980…14421399877292881921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.952 Γ— 10⁹⁷(98-digit number)
19529894962309651996…28842799754585763841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.905 Γ— 10⁹⁷(98-digit number)
39059789924619303992…57685599509171527681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.811 Γ— 10⁹⁷(98-digit number)
78119579849238607984…15371199018343055361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.562 Γ— 10⁹⁸(99-digit number)
15623915969847721596…30742398036686110721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.124 Γ— 10⁹⁸(99-digit number)
31247831939695443193…61484796073372221441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.249 Γ— 10⁹⁸(99-digit number)
62495663879390886387…22969592146744442881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.249 Γ— 10⁹⁹(100-digit number)
12499132775878177277…45939184293488885761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.499 Γ— 10⁹⁹(100-digit number)
24998265551756354555…91878368586977771521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.999 Γ— 10⁹⁹(100-digit number)
49996531103512709110…83756737173955543041
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,708,437 XPMΒ·at block #6,808,048 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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