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Block #545,737

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/15/2014, 12:53:31 PM Β· Difficulty 10.9542 Β· 6,261,982 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5540af913c2011cc67e433b790550910298c1be0e7ca7e3c7c0360f128eb4ff2
View on Chainz β†—

Height

#545,737

Difficulty

10.954170

Transactions

2

Size

1.68 KB

Version

2

Bits

0af44476

Nonce

36,877,392

Timestamp

5/15/2014, 12:53:31 PM

Confirmations

6,261,982

Mined by

⛏️ P2SHAG42cgncPU2D4D5uVeo9GtDW71oFohSJmJ

Merkle Root

8fb01c19e037283010a006ccf78583720d81146dd112640e534f063fe9aa5129
Transactions (2)
Coinbase335aca1be8f25e…07c5b8d7568c10
1 in β†’ 1 out8.3440 XPM109 B
AG42cgnc…oFohSJmJ
d63c2d3ede0a57…d81a07ff6cbba2
10 in β†’ 1 out75.6300 XPM1.49 KB
AREyP38c…DC4LiTCX
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.

1.062 Γ— 10⁹⁸(99-digit number)
10624998282973843344…31986806858898693121
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
1.062 Γ— 10⁹⁸(99-digit number)
10624998282973843344…31986806858898693121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.124 Γ— 10⁹⁸(99-digit number)
21249996565947686689…63973613717797386241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.249 Γ— 10⁹⁸(99-digit number)
42499993131895373379…27947227435594772481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.499 Γ— 10⁹⁸(99-digit number)
84999986263790746759…55894454871189544961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.699 Γ— 10⁹⁹(100-digit number)
16999997252758149351…11788909742379089921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.399 Γ— 10⁹⁹(100-digit number)
33999994505516298703…23577819484758179841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.799 Γ— 10⁹⁹(100-digit number)
67999989011032597407…47155638969516359681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.359 Γ— 10¹⁰⁰(101-digit number)
13599997802206519481…94311277939032719361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.719 Γ— 10¹⁰⁰(101-digit number)
27199995604413038963…88622555878065438721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.439 Γ— 10¹⁰⁰(101-digit number)
54399991208826077926…77245111756130877441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.087 Γ— 10¹⁰¹(102-digit number)
10879998241765215585…54490223512261754881
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,705,785 XPMΒ·at block #6,807,718 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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