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Block #1,426,942

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/25/2016, 12:04:37 AM Β· Difficulty 10.7536 Β· 5,418,445 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
63566cb6f558f0f2508cfcf838588e72ba9ffe7ceb12845efcc138e300e0e5cf
View on Chainz β†—

Height

#1,426,942

Difficulty

10.753620

Transactions

1

Size

199 B

Version

2

Bits

0ac0ed38

Nonce

316,278,534

Timestamp

1/25/2016, 12:04:37 AM

Confirmations

5,418,445

Mined by

⛏️ P2SHANA1iWer3yxRpzuxAYqoEW1YEd1G511PAw

Merkle Root

3552d6862add3237fe7fd54e2da375caf7d03ebaa74892f56e1433896ed55e94
Transactions (1)
Coinbase3552d6862add32…1433896ed55e94
1 in β†’ 1 out8.6300 XPM109 B
ANA1iWer…1G511PAw
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.

2.743 Γ— 10⁹⁴(95-digit number)
27431471730191992733…94933869503636982399
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.743 Γ— 10⁹⁴(95-digit number)
27431471730191992733…94933869503636982399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.486 Γ— 10⁹⁴(95-digit number)
54862943460383985467…89867739007273964799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.097 Γ— 10⁹⁡(96-digit number)
10972588692076797093…79735478014547929599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.194 Γ— 10⁹⁡(96-digit number)
21945177384153594187…59470956029095859199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.389 Γ— 10⁹⁡(96-digit number)
43890354768307188374…18941912058191718399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.778 Γ— 10⁹⁡(96-digit number)
87780709536614376748…37883824116383436799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.755 Γ— 10⁹⁢(97-digit number)
17556141907322875349…75767648232766873599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.511 Γ— 10⁹⁢(97-digit number)
35112283814645750699…51535296465533747199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.022 Γ— 10⁹⁢(97-digit number)
70224567629291501398…03070592931067494399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.404 Γ— 10⁹⁷(98-digit number)
14044913525858300279…06141185862134988799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.808 Γ— 10⁹⁷(98-digit number)
28089827051716600559…12282371724269977599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:58,007,541 XPMΒ·at block #6,845,386 Β· updates every 60s
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