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Block #104,507

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/8/2013, 2:19:26 AM Β· Difficulty 9.5582 Β· 6,721,874 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f4e292166254907415c9f26f2593146fceabfe5da1863bebe0cea900bf7b39da
View on Chainz β†—

Height

#104,507

Difficulty

9.558238

Transactions

1

Size

199 B

Version

2

Bits

098ee8aa

Nonce

19,048

Timestamp

8/8/2013, 2:19:26 AM

Confirmations

6,721,874

Mined by

⛏️ P2SHAUxVBxEZXDB6yUg6g3i67L1Ck5K62C9akR

Merkle Root

98cfaa147b033f3a9010c14aa6e72c602ddd768807bc03040fa838cdda89f5e5
Transactions (1)
Coinbase98cfaa147b033f…a838cdda89f5e5
1 in β†’ 1 out10.9300 XPM109 B
AUxVBxEZ…K62C9akR
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.

1.160 Γ— 10⁹⁡(96-digit number)
11604761429051188183…58075751034891841041
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
1.160 Γ— 10⁹⁡(96-digit number)
11604761429051188183…58075751034891841041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.320 Γ— 10⁹⁡(96-digit number)
23209522858102376367…16151502069783682081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.641 Γ— 10⁹⁡(96-digit number)
46419045716204752735…32303004139567364161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.283 Γ— 10⁹⁡(96-digit number)
92838091432409505471…64606008279134728321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.856 Γ— 10⁹⁢(97-digit number)
18567618286481901094…29212016558269456641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.713 Γ— 10⁹⁢(97-digit number)
37135236572963802188…58424033116538913281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.427 Γ— 10⁹⁢(97-digit number)
74270473145927604377…16848066233077826561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.485 Γ— 10⁹⁷(98-digit number)
14854094629185520875…33696132466155653121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.970 Γ— 10⁹⁷(98-digit number)
29708189258371041751…67392264932311306241
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:57,855,194 XPMΒ·at block #6,826,380 Β· updates every 60s
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