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Block #43,525

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 9:12:43 PM Β· Difficulty 8.6683 Β· 6,773,171 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
79c2a2f4bc2d3d432e8d0764b29f1d1696079fee52ea5c2767e9b7350afc63bf
View on Chainz β†—

Height

#43,525

Difficulty

8.668278

Transactions

1

Size

198 B

Version

2

Bits

08ab144c

Nonce

488

Timestamp

7/14/2013, 9:12:43 PM

Confirmations

6,773,171

Mined by

⛏️ P2SHAenRVgCKhbGVbbasvd2WAmMywRhv1UUmj4

Merkle Root

142c469b497d3b52797ff514a2703bbf7825428deff7e1d74410027d75bcf572
Transactions (1)
Coinbase142c469b497d3b…10027d75bcf572
1 in β†’ 1 out13.2900 XPM109 B
AenRVgCK…hv1UUmj4
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.

2.328 Γ— 10⁹³(94-digit number)
23281887514411423209…62403483066376455779
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
2.328 Γ— 10⁹³(94-digit number)
23281887514411423209…62403483066376455779
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.328 Γ— 10⁹³(94-digit number)
23281887514411423209…62403483066376455781
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
4.656 Γ— 10⁹³(94-digit number)
46563775028822846418…24806966132752911559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.656 Γ— 10⁹³(94-digit number)
46563775028822846418…24806966132752911561
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
9.312 Γ— 10⁹³(94-digit number)
93127550057645692837…49613932265505823119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.312 Γ— 10⁹³(94-digit number)
93127550057645692837…49613932265505823121
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
1.862 Γ— 10⁹⁴(95-digit number)
18625510011529138567…99227864531011646239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.862 Γ— 10⁹⁴(95-digit number)
18625510011529138567…99227864531011646241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

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 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:57,777,690 XPMΒ·at block #6,816,695 Β· updates every 60s
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