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Block #850,746

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/12/2014, 6:13:12 PM Β· Difficulty 10.9712 Β· 5,982,166 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7075788dd36d66aa9fa5ce84547e5ff13b2a7467ee924a69e04de954ba86449d
View on Chainz β†—

Height

#850,746

Difficulty

10.971171

Transactions

3

Size

657 B

Version

2

Bits

0af89ea4

Nonce

1,370,194,214

Timestamp

12/12/2014, 6:13:12 PM

Confirmations

5,982,166

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f6e845dfd6d9e4768b96e9c8488cf38b3a3bd88e53a1b84588659226a0a14733
Transactions (3)
Coinbase80a77585e763e5…254fa5d4cb6659
1 in β†’ 1 out8.3150 XPM116 B
ANSXnLY2…Sd25TjkD
efcdf5e19d904b…23067d3876ceb5
1 in β†’ 2 out6.1478 XPM226 B
AZ6ngte8…E6BKEyyGAHRoBSh4…BSVTQ36Q
06383d0c442074…50130f21650b6f
1 in β†’ 2 out0.0476 XPM225 B
ASwHG5aZ…HHwCWU7mAHxss7ej…32gakAxr
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.

6.944 Γ— 10⁹⁡(96-digit number)
69443949196161461721…96380825468203756681
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
6.944 Γ— 10⁹⁡(96-digit number)
69443949196161461721…96380825468203756681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.388 Γ— 10⁹⁢(97-digit number)
13888789839232292344…92761650936407513361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.777 Γ— 10⁹⁢(97-digit number)
27777579678464584688…85523301872815026721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.555 Γ— 10⁹⁢(97-digit number)
55555159356929169377…71046603745630053441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.111 Γ— 10⁹⁷(98-digit number)
11111031871385833875…42093207491260106881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.222 Γ— 10⁹⁷(98-digit number)
22222063742771667751…84186414982520213761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.444 Γ— 10⁹⁷(98-digit number)
44444127485543335502…68372829965040427521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.888 Γ— 10⁹⁷(98-digit number)
88888254971086671004…36745659930080855041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.777 Γ— 10⁹⁸(99-digit number)
17777650994217334200…73491319860161710081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.555 Γ— 10⁹⁸(99-digit number)
35555301988434668401…46982639720323420161
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:57,907,468 XPMΒ·at block #6,832,911 Β· updates every 60s
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