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Block #1,487,934

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/7/2016, 9:13:41 PM Β· Difficulty 10.7164 Β· 5,336,717 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bb9831162f8e09c07ff383661e837132ee22cb29d146c15dcead55dfad17194f
View on Chainz β†—

Height

#1,487,934

Difficulty

10.716438

Transactions

1

Size

200 B

Version

2

Bits

0ab76878

Nonce

1,033,350,022

Timestamp

3/7/2016, 9:13:41 PM

Confirmations

5,336,717

Mined by

⛏️ P2SHAPdZ8xWT1DxmH95qiJ7y1V7goX9nKuq5eA

Merkle Root

c94a1f6bb824e0620a244fe32202d22c2ee8cc3fc3bd0d1ac25f8309dae496a8
Transactions (1)
Coinbasec94a1f6bb824e0…5f8309dae496a8
1 in β†’ 1 out8.6900 XPM110 B
APdZ8xWT…9nKuq5eA
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.

1.173 Γ— 10⁹⁡(96-digit number)
11735562048171555605…53421548244308242161
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
1.173 Γ— 10⁹⁡(96-digit number)
11735562048171555605…53421548244308242161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.347 Γ— 10⁹⁡(96-digit number)
23471124096343111211…06843096488616484321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.694 Γ— 10⁹⁡(96-digit number)
46942248192686222422…13686192977232968641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.388 Γ— 10⁹⁡(96-digit number)
93884496385372444844…27372385954465937281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.877 Γ— 10⁹⁢(97-digit number)
18776899277074488968…54744771908931874561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.755 Γ— 10⁹⁢(97-digit number)
37553798554148977937…09489543817863749121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.510 Γ— 10⁹⁢(97-digit number)
75107597108297955875…18979087635727498241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.502 Γ— 10⁹⁷(98-digit number)
15021519421659591175…37958175271454996481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.004 Γ— 10⁹⁷(98-digit number)
30043038843319182350…75916350542909992961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.008 Γ— 10⁹⁷(98-digit number)
60086077686638364700…51832701085819985921
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:57,841,273 XPMΒ·at block #6,824,650 Β· updates every 60s
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