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Block #1,249,881

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/23/2015, 4:17:41 PM Β· Difficulty 10.7700 Β· 5,566,783 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c307a34be120e599e4bfdd43ec84943671e3f3dab0e097a46265932f546dbac7
View on Chainz β†—

Height

#1,249,881

Difficulty

10.770021

Transactions

2

Size

425 B

Version

2

Bits

0ac52013

Nonce

782,949,382

Timestamp

9/23/2015, 4:17:41 PM

Confirmations

5,566,783

Mined by

⛏️ P2SHAcKB7yQTFkwQ8nSFxiBqHLXTFfxf1A6tCV

Merkle Root

5d7194147256b39991b9c5c32a514409383d9838dce38c64b0b8b5b85c3bf4b6
Transactions (2)
Coinbase0bcdd7f30e8537…b7534568eea4ec
1 in β†’ 1 out8.6200 XPM109 B
AcKB7yQT…xf1A6tCV
6c44b79e99daf7…47d06b29896cd7
1 in β†’ 2 out0.7918 XPM226 B
AeBwvm57…kL6E7ayFAYECntTn…VwTRWLbt
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.

2.141 Γ— 10⁹⁡(96-digit number)
21419539669857813961…33543180031287453441
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
2.141 Γ— 10⁹⁡(96-digit number)
21419539669857813961…33543180031287453441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.283 Γ— 10⁹⁡(96-digit number)
42839079339715627923…67086360062574906881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.567 Γ— 10⁹⁡(96-digit number)
85678158679431255846…34172720125149813761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.713 Γ— 10⁹⁢(97-digit number)
17135631735886251169…68345440250299627521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.427 Γ— 10⁹⁢(97-digit number)
34271263471772502338…36690880500599255041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.854 Γ— 10⁹⁢(97-digit number)
68542526943545004677…73381761001198510081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.370 Γ— 10⁹⁷(98-digit number)
13708505388709000935…46763522002397020161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.741 Γ— 10⁹⁷(98-digit number)
27417010777418001870…93527044004794040321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.483 Γ— 10⁹⁷(98-digit number)
54834021554836003741…87054088009588080641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.096 Γ— 10⁹⁸(99-digit number)
10966804310967200748…74108176019176161281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.193 Γ— 10⁹⁸(99-digit number)
21933608621934401496…48216352038352322561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
4.386 Γ— 10⁹⁸(99-digit number)
43867217243868802993…96432704076704645121
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,777,431 XPMΒ·at block #6,816,663 Β· updates every 60s
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