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Block #565,242

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/28/2014, 5:01:18 AM Β· Difficulty 10.9649 Β· 6,245,837 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
fc21c34af269609978b5c0a192cbd7fede680d1d35b44714716f7c0df42a2ad0
View on Chainz β†—

Height

#565,242

Difficulty

10.964862

Transactions

2

Size

1.72 KB

Version

2

Bits

0af70132

Nonce

680,823,825

Timestamp

5/28/2014, 5:01:18 AM

Confirmations

6,245,837

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7652c13d15c8820e0f1f180b383dce3fa613a529d1bff58b127e9b676de9787e
Transactions (2)
Coinbase34850435e61bc6…d67cb885c9ac17
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
c37eb92f8c1752…5b62a603e460ab
10 in β†’ 2 out9.0269 XPM1.52 KB
AHr5Po7k…wMB6iUt2AdgTue2S…eATPjg5V
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.

1.353 Γ— 10⁹⁸(99-digit number)
13538302684560586355…69600153734925369919
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.353 Γ— 10⁹⁸(99-digit number)
13538302684560586355…69600153734925369919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.353 Γ— 10⁹⁸(99-digit number)
13538302684560586355…69600153734925369921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.707 Γ— 10⁹⁸(99-digit number)
27076605369121172710…39200307469850739839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.707 Γ— 10⁹⁸(99-digit number)
27076605369121172710…39200307469850739841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
5.415 Γ— 10⁹⁸(99-digit number)
54153210738242345420…78400614939701479679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.415 Γ— 10⁹⁸(99-digit number)
54153210738242345420…78400614939701479681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.083 Γ— 10⁹⁹(100-digit number)
10830642147648469084…56801229879402959359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.083 Γ— 10⁹⁹(100-digit number)
10830642147648469084…56801229879402959361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.166 Γ— 10⁹⁹(100-digit number)
21661284295296938168…13602459758805918719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.166 Γ— 10⁹⁹(100-digit number)
21661284295296938168…13602459758805918721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.332 Γ— 10⁹⁹(100-digit number)
43322568590593876336…27204919517611837439
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,732,738 XPMΒ·at block #6,811,078 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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