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Block #105,087

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2013, 8:55:51 AM Β· Difficulty 9.5741 Β· 6,705,528 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5ebce27c7e7e3332872c3f7f115e90dc327f2815a72fbddda10cf90ce90ff4c2
View on Chainz β†—

Height

#105,087

Difficulty

9.574071

Transactions

2

Size

621 B

Version

2

Bits

0992f659

Nonce

45,386

Timestamp

8/8/2013, 8:55:51 AM

Confirmations

6,705,528

Mined by

⛏️ P2SHASXW8s4r1QTq8Djg6zDrh4WCnULM8vqY9U

Merkle Root

4576bbf2d98ca4858501d41cf1c280a769856c866915e96bdff5c6dd0a6abcdd
Transactions (2)
Coinbased39056edd136ca…3d5466158424b5
1 in β†’ 1 out10.9000 XPM109 B
ASXW8s4r…LM8vqY9U
be24f768e3948e…12e24f71fd70b6
3 in β†’ 1 out22.6000 XPM421 B
AcS31cBK…Dmi7rdMj
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.

5.640 Γ— 10⁹⁷(98-digit number)
56406731084501505797…84899518070950301929
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
5.640 Γ— 10⁹⁷(98-digit number)
56406731084501505797…84899518070950301929
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.128 Γ— 10⁹⁸(99-digit number)
11281346216900301159…69799036141900603859
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.256 Γ— 10⁹⁸(99-digit number)
22562692433800602319…39598072283801207719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.512 Γ— 10⁹⁸(99-digit number)
45125384867601204638…79196144567602415439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.025 Γ— 10⁹⁸(99-digit number)
90250769735202409276…58392289135204830879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.805 Γ— 10⁹⁹(100-digit number)
18050153947040481855…16784578270409661759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.610 Γ— 10⁹⁹(100-digit number)
36100307894080963710…33569156540819323519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.220 Γ— 10⁹⁹(100-digit number)
72200615788161927420…67138313081638647039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.444 Γ— 10¹⁰⁰(101-digit number)
14440123157632385484…34276626163277294079
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,729,004 XPMΒ·at block #6,810,614 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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