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Block #54,266

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/16/2013, 7:32:19 PM Β· Difficulty 8.9318 Β· 6,741,338 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a52c96ed05c6fe946c438a9ed07d779f7068d75d66c244f5795d1cbbadca0b01
View on Chainz β†—

Height

#54,266

Difficulty

8.931815

Transactions

1

Size

201 B

Version

2

Bits

08ee8b6b

Nonce

228

Timestamp

7/16/2013, 7:32:19 PM

Confirmations

6,741,338

Mined by

⛏️ P2SHAK3X8M4n8p5BPtkuFf8v6T3hAuzFeMdGCF

Merkle Root

ad664b04da3c09247d329aa2581b739da8a73f9e51d98a51bfeb30fc9a0675ea
Transactions (1)
Coinbasead664b04da3c09…eb30fc9a0675ea
1 in β†’ 1 out12.5200 XPM110 B
AK3X8M4n…zFeMdGCF
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.

1.401 Γ— 10⁹⁸(99-digit number)
14015006362086442743…37106156674137057779
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
1.401 Γ— 10⁹⁸(99-digit number)
14015006362086442743…37106156674137057779
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.401 Γ— 10⁹⁸(99-digit number)
14015006362086442743…37106156674137057781
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
2.803 Γ— 10⁹⁸(99-digit number)
28030012724172885487…74212313348274115559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.803 Γ— 10⁹⁸(99-digit number)
28030012724172885487…74212313348274115561
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
5.606 Γ— 10⁹⁸(99-digit number)
56060025448345770975…48424626696548231119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.606 Γ— 10⁹⁸(99-digit number)
56060025448345770975…48424626696548231121
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
1.121 Γ— 10⁹⁹(100-digit number)
11212005089669154195…96849253393096462239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.121 Γ— 10⁹⁹(100-digit number)
11212005089669154195…96849253393096462241
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
2.242 Γ— 10⁹⁹(100-digit number)
22424010179338308390…93698506786192924479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,608,895 XPMΒ·at block #6,795,603 Β· updates every 60s
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