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Block #105,537

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/8/2013, 1:57:14 PM Β· Difficulty 9.5865 Β· 6,697,014 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
49ad04e52bc25a6c89bdace349d308c729f857b7eaa5f98b427daa0df7181a4b
View on Chainz β†—

Height

#105,537

Difficulty

9.586471

Transactions

1

Size

200 B

Version

2

Bits

099622f4

Nonce

128,977

Timestamp

8/8/2013, 1:57:14 PM

Confirmations

6,697,014

Mined by

⛏️ P2SHAL4on7MoehvKsN2qMpn6JMVQDzcZpCa12j

Merkle Root

eb8e58f776b2d25ef69960e2ea4fddb2c1f4e065409e86c8f6f1abe917d63573
Transactions (1)
Coinbaseeb8e58f776b2d2…f1abe917d63573
1 in β†’ 1 out10.8700 XPM109 B
AL4on7Mo…cZpCa12j
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.

1.082 Γ— 10⁹⁸(99-digit number)
10824503093748076155…07028646387976623721
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
1.082 Γ— 10⁹⁸(99-digit number)
10824503093748076155…07028646387976623721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.164 Γ— 10⁹⁸(99-digit number)
21649006187496152310…14057292775953247441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.329 Γ— 10⁹⁸(99-digit number)
43298012374992304621…28114585551906494881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.659 Γ— 10⁹⁸(99-digit number)
86596024749984609243…56229171103812989761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.731 Γ— 10⁹⁹(100-digit number)
17319204949996921848…12458342207625979521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.463 Γ— 10⁹⁹(100-digit number)
34638409899993843697…24916684415251959041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.927 Γ— 10⁹⁹(100-digit number)
69276819799987687394…49833368830503918081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.385 Γ— 10¹⁰⁰(101-digit number)
13855363959997537478…99666737661007836161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.771 Γ— 10¹⁰⁰(101-digit number)
27710727919995074957…99333475322015672321
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,664,420 XPMΒ·at block #6,802,550 Β· updates every 60s
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