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Block #338,663

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/1/2014, 2:18:09 PM Β· Difficulty 10.1104 Β· 6,488,413 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9a4b4b8b08e2cc217877a63fcc267f855eb345190dab466b8275a1265a55b92a
View on Chainz β†—

Height

#338,663

Difficulty

10.110385

Transactions

1

Size

200 B

Version

2

Bits

0a1c422c

Nonce

111,693

Timestamp

1/1/2014, 2:18:09 PM

Confirmations

6,488,413

Mined by

⛏️ P2SHATbpMT6acH6zFR9ea5eC8czg6TTsSzntas

Merkle Root

5f1bc2c71511bd2338401823fcfd3df0f70d350de9f00fe4239138ac48348ecc
Transactions (1)
Coinbase5f1bc2c71511bd…9138ac48348ecc
1 in β†’ 1 out9.7700 XPM109 B
ATbpMT6a…TsSzntas
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.

2.984 Γ— 10⁹⁷(98-digit number)
29843696898409013844…43906475427941832641
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
2.984 Γ— 10⁹⁷(98-digit number)
29843696898409013844…43906475427941832641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.968 Γ— 10⁹⁷(98-digit number)
59687393796818027689…87812950855883665281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.193 Γ— 10⁹⁸(99-digit number)
11937478759363605537…75625901711767330561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.387 Γ— 10⁹⁸(99-digit number)
23874957518727211075…51251803423534661121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.774 Γ— 10⁹⁸(99-digit number)
47749915037454422151…02503606847069322241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.549 Γ— 10⁹⁸(99-digit number)
95499830074908844302…05007213694138644481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.909 Γ— 10⁹⁹(100-digit number)
19099966014981768860…10014427388277288961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.819 Γ— 10⁹⁹(100-digit number)
38199932029963537720…20028854776554577921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.639 Γ— 10⁹⁹(100-digit number)
76399864059927075441…40057709553109155841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.527 Γ— 10¹⁰⁰(101-digit number)
15279972811985415088…80115419106218311681
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:57,860,792 XPMΒ·at block #6,827,075 Β· updates every 60s
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