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Block #1,033,775

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/26/2015, 5:04:05 PM Β· Difficulty 10.7493 Β· 5,774,850 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d05af2ca40d576101ebe5deb6d538f6d25e1a01ae3564e527d11254392d93205
View on Chainz β†—

Height

#1,033,775

Difficulty

10.749270

Transactions

3

Size

797 B

Version

2

Bits

0abfd027

Nonce

241,432,157

Timestamp

4/26/2015, 5:04:05 PM

Confirmations

5,774,850

Mined by

⛏️ P2SHAUyK89x6F7LWjk9Bw7DkVA6FWHgUrUpC13

Merkle Root

b32b8bd4b6347f8716a8af078565d21d772a2c2cc63cb23d9dd146dde4b975b6
Transactions (3)
Coinbaseba5c732d8afb82…67c92c71f2bee2
1 in β†’ 1 out8.6600 XPM109 B
AUyK89x6…gUrUpC13
8757ad3f4d5c81…55a6e692792bfc
2 in β†’ 2 out16.1075 XPM373 B
AU4f4km9…u8UnNcJ8AUKkNwm1…2vuAdTtX
5640ea6dbee05a…137459e559d3b9
1 in β†’ 2 out0.5449 XPM225 B
AWACRgn1…HV1FC58HAVVd94vJ…pW4YWuwZ
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.

7.588 Γ— 10⁹⁴(95-digit number)
75882573729416813784…26267623297213515521
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
7.588 Γ— 10⁹⁴(95-digit number)
75882573729416813784…26267623297213515521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.517 Γ— 10⁹⁡(96-digit number)
15176514745883362756…52535246594427031041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.035 Γ— 10⁹⁡(96-digit number)
30353029491766725513…05070493188854062081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.070 Γ— 10⁹⁡(96-digit number)
60706058983533451027…10140986377708124161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.214 Γ— 10⁹⁢(97-digit number)
12141211796706690205…20281972755416248321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.428 Γ— 10⁹⁢(97-digit number)
24282423593413380411…40563945510832496641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.856 Γ— 10⁹⁢(97-digit number)
48564847186826760822…81127891021664993281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.712 Γ— 10⁹⁢(97-digit number)
97129694373653521644…62255782043329986561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.942 Γ— 10⁹⁷(98-digit number)
19425938874730704328…24511564086659973121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.885 Γ— 10⁹⁷(98-digit number)
38851877749461408657…49023128173319946241
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:57,713,051 XPMΒ·at block #6,808,624 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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