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Block #1,534,611

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/10/2016, 8:47:51 AM Β· Difficulty 10.6174 Β· 5,273,949 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
62212b90dbdf9a87b1ab425be62313859eedbe6cd5300e8b3dfe615568790a4b
View on Chainz β†—

Height

#1,534,611

Difficulty

10.617428

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9e0fc4

Nonce

1,364,074,533

Timestamp

4/10/2016, 8:47:51 AM

Confirmations

5,273,949

Mined by

⛏️ P2SHAJSczq9FANJ4TTHnSZRjqeTEzr2xk8vgBZ

Merkle Root

10a69e2722744f0e4168a6f33db3299f97aedc7c47866d6c7f5cb407638be7f9
Transactions (2)
Coinbase828db09fb1c150…43a9284dd39477
1 in β†’ 1 out8.9400 XPM109 B
AJSczq9F…2xk8vgBZ
b8438dd39f6d1c…9bd5064f6b5b43
51 in β†’ 1 out2959.0639 XPM7.42 KB
AH46BmnJ…mDknQ1bq
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.

1.318 Γ— 10⁹⁢(97-digit number)
13181703266326221556…76647581923326719999
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.318 Γ— 10⁹⁢(97-digit number)
13181703266326221556…76647581923326719999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.636 Γ— 10⁹⁢(97-digit number)
26363406532652443112…53295163846653439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.272 Γ— 10⁹⁢(97-digit number)
52726813065304886225…06590327693306879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.054 Γ— 10⁹⁷(98-digit number)
10545362613060977245…13180655386613759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.109 Γ— 10⁹⁷(98-digit number)
21090725226121954490…26361310773227519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.218 Γ— 10⁹⁷(98-digit number)
42181450452243908980…52722621546455039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.436 Γ— 10⁹⁷(98-digit number)
84362900904487817960…05445243092910079999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.687 Γ— 10⁹⁸(99-digit number)
16872580180897563592…10890486185820159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.374 Γ— 10⁹⁸(99-digit number)
33745160361795127184…21780972371640319999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.749 Γ— 10⁹⁸(99-digit number)
67490320723590254368…43561944743280639999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,712,538 XPMΒ·at block #6,808,559 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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