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Block #2,053,208

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/4/2017, 1:57:00 AM Β· Difficulty 10.7646 Β· 4,751,855 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
137ac1a3289b3a033c220c415a50392428c209c655d7b0f5698299f6d7b8f6f5
View on Chainz β†—

Height

#2,053,208

Difficulty

10.764558

Transactions

2

Size

872 B

Version

2

Bits

0ac3ba15

Nonce

422,164,180

Timestamp

4/4/2017, 1:57:00 AM

Confirmations

4,751,855

Mined by

⛏️ P2SHAHHZsm9PawyUjKr6V69yB4YhqY9gGkrA8y

Merkle Root

54469ec93611ec267cf3e2ff049baa234f0c82736d976be328f81da49b88e257
Transactions (2)
Coinbase21768ef98a49c8…2dda6ecbeecf6b
1 in β†’ 1 out8.6300 XPM110 B
AHHZsm9P…9gGkrA8y
cad3a15657cf21…f33dbdf37dcd58
4 in β†’ 2 out4204.4717 XPM672 B
AQfgY5G1…r68d4iFfAGzhAFUv…Hozi1kTu
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.

6.994 Γ— 10⁹⁴(95-digit number)
69942171865119695339…21507948539036257441
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
6.994 Γ— 10⁹⁴(95-digit number)
69942171865119695339…21507948539036257441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.398 Γ— 10⁹⁡(96-digit number)
13988434373023939067…43015897078072514881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.797 Γ— 10⁹⁡(96-digit number)
27976868746047878135…86031794156145029761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.595 Γ— 10⁹⁡(96-digit number)
55953737492095756271…72063588312290059521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.119 Γ— 10⁹⁢(97-digit number)
11190747498419151254…44127176624580119041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.238 Γ— 10⁹⁢(97-digit number)
22381494996838302508…88254353249160238081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.476 Γ— 10⁹⁢(97-digit number)
44762989993676605017…76508706498320476161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.952 Γ— 10⁹⁢(97-digit number)
89525979987353210034…53017412996640952321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.790 Γ— 10⁹⁷(98-digit number)
17905195997470642006…06034825993281904641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.581 Γ— 10⁹⁷(98-digit number)
35810391994941284013…12069651986563809281
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:57,684,570 XPMΒ·at block #6,805,062 Β· updates every 60s
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