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Block #270,795

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/24/2013, 5:19:07 AM Β· Difficulty 9.9515 Β· 6,545,963 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a37f34b1dd2dd94f1ffe52a4766d8f1ff45416141819ca41513399fc857552c6
View on Chainz β†—

Height

#270,795

Difficulty

9.951476

Transactions

2

Size

1.28 KB

Version

2

Bits

09f393e7

Nonce

95,227

Timestamp

11/24/2013, 5:19:07 AM

Confirmations

6,545,963

Mined by

⛏️ P2SHAZ3QfoPpnVYeEusuAfEMBMTTLhGUEn9BM7

Merkle Root

d49c22c2ed787a4e7ad3f8ab4eed7cd4c3d81111e7894e084606b7a0f19debf7
Transactions (2)
Coinbase6a8f7ece05b4c4…8f2c94c2147ad7
1 in β†’ 1 out10.1000 XPM109 B
AZ3QfoPp…GUEn9BM7
b0ab2ff8e3c008…14269c7792fa08
7 in β†’ 2 out15.9106 XPM1.09 KB
AYLZvsSe…jbekUhorAMSj35t4…12GtKPQA
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.

2.686 Γ— 10⁹⁴(95-digit number)
26866275804050287817…70247814624115045119
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
2.686 Γ— 10⁹⁴(95-digit number)
26866275804050287817…70247814624115045119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.686 Γ— 10⁹⁴(95-digit number)
26866275804050287817…70247814624115045121
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
5.373 Γ— 10⁹⁴(95-digit number)
53732551608100575635…40495629248230090239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.373 Γ— 10⁹⁴(95-digit number)
53732551608100575635…40495629248230090241
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
1.074 Γ— 10⁹⁡(96-digit number)
10746510321620115127…80991258496460180479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.074 Γ— 10⁹⁡(96-digit number)
10746510321620115127…80991258496460180481
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
2.149 Γ— 10⁹⁡(96-digit number)
21493020643240230254…61982516992920360959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.149 Γ— 10⁹⁡(96-digit number)
21493020643240230254…61982516992920360961
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
4.298 Γ— 10⁹⁡(96-digit number)
42986041286480460508…23965033985840721919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.298 Γ— 10⁹⁡(96-digit number)
42986041286480460508…23965033985840721921
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
8.597 Γ— 10⁹⁡(96-digit number)
85972082572960921016…47930067971681443839
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:57,778,095 XPMΒ·at block #6,816,757 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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