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Block #38,188

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 11:41:27 AM Β· Difficulty 8.1458 Β· 6,778,121 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
63426f4249591b715d510b2bd9ac9f57b621a63785af1183c7ba08ad6771bf30
View on Chainz β†—

Height

#38,188

Difficulty

8.145774

Transactions

1

Size

199 B

Version

2

Bits

0825516e

Nonce

310

Timestamp

7/14/2013, 11:41:27 AM

Confirmations

6,778,121

Mined by

⛏️ P2SHAYCQsY6D71QgyTLoRYWSvnZpmJsFr8Cxp5

Merkle Root

6335d1799856a89a2f436139bdcc1f679f6fb3ef810511df9321b6eca3f1501b
Transactions (1)
Coinbase6335d1799856a8…21b6eca3f1501b
1 in β†’ 1 out15.0500 XPM110 B
AYCQsY6D…sFr8Cxp5
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.

2.037 Γ— 10⁹¹(92-digit number)
20379961271866347059…49520130654910565469
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
2.037 Γ— 10⁹¹(92-digit number)
20379961271866347059…49520130654910565469
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.037 Γ— 10⁹¹(92-digit number)
20379961271866347059…49520130654910565471
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
4.075 Γ— 10⁹¹(92-digit number)
40759922543732694118…99040261309821130939
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.075 Γ— 10⁹¹(92-digit number)
40759922543732694118…99040261309821130941
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
8.151 Γ— 10⁹¹(92-digit number)
81519845087465388236…98080522619642261879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.151 Γ— 10⁹¹(92-digit number)
81519845087465388236…98080522619642261881
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
1.630 Γ— 10⁹²(93-digit number)
16303969017493077647…96161045239284523759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.630 Γ— 10⁹²(93-digit number)
16303969017493077647…96161045239284523761
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:57,774,592 XPMΒ·at block #6,816,308 Β· updates every 60s
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