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Block #1,470,841

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/24/2016, 11:07:36 PM Β· Difficulty 10.7198 Β· 5,363,000 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fbe9712f25868bdf7a39659a1725ee9cd6fb911263f83e08844efa6db03cda53
View on Chainz β†—

Height

#1,470,841

Difficulty

10.719821

Transactions

2

Size

3.74 KB

Version

2

Bits

0ab8462c

Nonce

805,381,742

Timestamp

2/24/2016, 11:07:36 PM

Confirmations

5,363,000

Mined by

⛏️ P2SHAP4qPvxEB2fuGFZLz2b9USuhnLzpEM8Qn2

Merkle Root

2ec0b3cfbaf357e27d82dd2091e179258cb1820bf053aa6fc54691d8a07a8059
Transactions (2)
Coinbase02ab4162ace861…0592136146de04
1 in β†’ 1 out8.7600 XPM109 B
AP4qPvxE…zpEM8Qn2
d7f68e5f20375d…7dd9dd9da751d7
24 in β†’ 2 out183.8883 XPM3.54 KB
AXaxJB85…3kXfMDzCAKG6Dtxq…5kLV5BZg
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.

3.639 Γ— 10⁹⁡(96-digit number)
36394201195934677205…84690399342778919999
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
3.639 Γ— 10⁹⁡(96-digit number)
36394201195934677205…84690399342778919999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.278 Γ— 10⁹⁡(96-digit number)
72788402391869354411…69380798685557839999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.455 Γ— 10⁹⁢(97-digit number)
14557680478373870882…38761597371115679999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.911 Γ— 10⁹⁢(97-digit number)
29115360956747741764…77523194742231359999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.823 Γ— 10⁹⁢(97-digit number)
58230721913495483529…55046389484462719999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.164 Γ— 10⁹⁷(98-digit number)
11646144382699096705…10092778968925439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.329 Γ— 10⁹⁷(98-digit number)
23292288765398193411…20185557937850879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.658 Γ— 10⁹⁷(98-digit number)
46584577530796386823…40371115875701759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.316 Γ— 10⁹⁷(98-digit number)
93169155061592773647…80742231751403519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.863 Γ— 10⁹⁸(99-digit number)
18633831012318554729…61484463502807039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.726 Γ— 10⁹⁸(99-digit number)
37267662024637109458…22968927005614079999
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:57,914,957 XPMΒ·at block #6,833,840 Β· updates every 60s
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