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Block #2,050,154

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/2/2017, 8:55:10 PM Β· Difficulty 10.6946 Β· 4,783,578 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1ea20658dd71662fbf04fe25773739c2c9f26f48b19fde1c2a9303de28067f07
View on Chainz β†—

Height

#2,050,154

Difficulty

10.694643

Transactions

1

Size

210 B

Version

2

Bits

0ab1d426

Nonce

62,991,140

Timestamp

4/2/2017, 8:55:10 PM

Confirmations

4,783,578

Mined by

⛏️ jhPrimeminerAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

cc377a6c55387b7cef7d83166e43b8660606a8ebba34553e67f85cf704ffc786
Transactions (1)
Coinbasecc377a6c55387b…f85cf704ffc786
1 in β†’ 1 out8.7300 XPM118 B
AM6GYpjw…aw86QDtR
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.

7.278 Γ— 10⁹⁹(100-digit number)
72785073513603480150…00944873562509803519
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
7.278 Γ— 10⁹⁹(100-digit number)
72785073513603480150…00944873562509803519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.278 Γ— 10⁹⁹(100-digit number)
72785073513603480150…00944873562509803521
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
1.455 Γ— 10¹⁰⁰(101-digit number)
14557014702720696030…01889747125019607039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.455 Γ— 10¹⁰⁰(101-digit number)
14557014702720696030…01889747125019607041
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
2.911 Γ— 10¹⁰⁰(101-digit number)
29114029405441392060…03779494250039214079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.911 Γ— 10¹⁰⁰(101-digit number)
29114029405441392060…03779494250039214081
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
5.822 Γ— 10¹⁰⁰(101-digit number)
58228058810882784120…07558988500078428159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.822 Γ— 10¹⁰⁰(101-digit number)
58228058810882784120…07558988500078428161
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
1.164 Γ— 10¹⁰¹(102-digit number)
11645611762176556824…15117977000156856319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.164 Γ— 10¹⁰¹(102-digit number)
11645611762176556824…15117977000156856321
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:57,914,079 XPMΒ·at block #6,833,731 Β· updates every 60s
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