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Block #415,211

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/22/2014, 1:24:54 PM Β· Difficulty 10.4029 Β· 6,397,833 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
629a53fe3e7526a7baffb5a6e19fe029c78918a3107b92a4297f7fc842042b84
View on Chainz β†—

Height

#415,211

Difficulty

10.402861

Transactions

1

Size

200 B

Version

2

Bits

0a6721e4

Nonce

70,929

Timestamp

2/22/2014, 1:24:54 PM

Confirmations

6,397,833

Mined by

⛏️ P2SHAcH2s7Y4D9hVCSQQdA7jo9e2ue1nk8yDe6

Merkle Root

aa94b1a44ff5d2548ad4d982f538ebb1da37d7a5551286bb7110d2c706728668
Transactions (1)
Coinbaseaa94b1a44ff5d2…10d2c706728668
1 in β†’ 1 out9.2300 XPM109 B
AcH2s7Y4…1nk8yDe6
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.

3.739 Γ— 10⁹⁢(97-digit number)
37390789691791159853…44809411766107862911
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
3.739 Γ— 10⁹⁢(97-digit number)
37390789691791159853…44809411766107862911
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.478 Γ— 10⁹⁢(97-digit number)
74781579383582319707…89618823532215725821
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.495 Γ— 10⁹⁷(98-digit number)
14956315876716463941…79237647064431451641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.991 Γ— 10⁹⁷(98-digit number)
29912631753432927883…58475294128862903281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.982 Γ— 10⁹⁷(98-digit number)
59825263506865855766…16950588257725806561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.196 Γ— 10⁹⁸(99-digit number)
11965052701373171153…33901176515451613121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.393 Γ— 10⁹⁸(99-digit number)
23930105402746342306…67802353030903226241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.786 Γ— 10⁹⁸(99-digit number)
47860210805492684612…35604706061806452481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.572 Γ— 10⁹⁸(99-digit number)
95720421610985369225…71209412123612904961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.914 Γ— 10⁹⁹(100-digit number)
19144084322197073845…42418824247225809921
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:57,748,397 XPMΒ·at block #6,813,043 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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