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Block #294,520

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/4/2013, 10:09:40 PM Β· Difficulty 9.9911 Β· 6,519,298 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
535a135d1988a2a839562d5bb99e8eb922c21471e556bd5b688be4bf411253ef
View on Chainz β†—

Height

#294,520

Difficulty

9.991071

Transactions

2

Size

3.35 KB

Version

2

Bits

09fdb6d3

Nonce

263,429

Timestamp

12/4/2013, 10:09:40 PM

Confirmations

6,519,298

Mined by

⛏️ P2SHAQTKho5sGXU29XTwAveW8NXoKaRaFJrCYh

Merkle Root

031e1d854ad6be66145c97bbf905a842370fc6abdec7feb630354abdb4e1b421
Transactions (2)
Coinbase23d3541455dc2d…5750cb21b5a4ef
1 in β†’ 1 out10.0400 XPM109 B
AQTKho5s…RaFJrCYh
c1b513266a9859…2c26244dbbb9c9
28 in β†’ 1 out286.2700 XPM3.16 KB
AMWKfUWU…hjT6U8ko
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.

6.522 Γ— 10⁹⁡(96-digit number)
65221226634153901885…00452803631620675199
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
6.522 Γ— 10⁹⁡(96-digit number)
65221226634153901885…00452803631620675199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.522 Γ— 10⁹⁡(96-digit number)
65221226634153901885…00452803631620675201
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
1.304 Γ— 10⁹⁢(97-digit number)
13044245326830780377…00905607263241350399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.304 Γ— 10⁹⁢(97-digit number)
13044245326830780377…00905607263241350401
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
2.608 Γ— 10⁹⁢(97-digit number)
26088490653661560754…01811214526482700799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.608 Γ— 10⁹⁢(97-digit number)
26088490653661560754…01811214526482700801
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
5.217 Γ— 10⁹⁢(97-digit number)
52176981307323121508…03622429052965401599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.217 Γ— 10⁹⁢(97-digit number)
52176981307323121508…03622429052965401601
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
1.043 Γ— 10⁹⁷(98-digit number)
10435396261464624301…07244858105930803199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.043 Γ— 10⁹⁷(98-digit number)
10435396261464624301…07244858105930803201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,754,612 XPMΒ·at block #6,813,817 Β· updates every 60s
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