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Block #2,634,483

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 10:05:17 PM Β· Difficulty 11.2481 Β· 4,207,711 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1ce793034fe2aa5fd8ce8082bf36636d2d99ab6971dce272ba4555dc750724e4
View on Chainz β†—

Height

#2,634,483

Difficulty

11.248077

Transactions

2

Size

575 B

Version

2

Bits

0b3f81f2

Nonce

476,218,530

Timestamp

4/28/2018, 10:05:17 PM

Confirmations

4,207,711

Mined by

⛏️ P2SHAXCDRn4zpfQQpEeYGQaC5hnUXv6KH3bfqJ

Merkle Root

bd4ba4419bb22ce24206261a3bf93fd3154dc5a75a5d92b83f800cbff32e9b9b
Transactions (2)
Coinbased18b968c13f20c…574df2607b9e5c
1 in β†’ 1 out7.9000 XPM110 B
AXCDRn4z…6KH3bfqJ
ba1c60db1c5dc3…76d671e1577f0f
2 in β†’ 2 out1300.5198 XPM375 B
AGafMD9U…qUye8cWTAQkckRBB…w3Ze988s
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.

1.175 Γ— 10⁹⁡(96-digit number)
11754574755312505155…35017785579728324479
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
1.175 Γ— 10⁹⁡(96-digit number)
11754574755312505155…35017785579728324479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.175 Γ— 10⁹⁡(96-digit number)
11754574755312505155…35017785579728324481
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
2.350 Γ— 10⁹⁡(96-digit number)
23509149510625010310…70035571159456648959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.350 Γ— 10⁹⁡(96-digit number)
23509149510625010310…70035571159456648961
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
4.701 Γ— 10⁹⁡(96-digit number)
47018299021250020621…40071142318913297919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.701 Γ— 10⁹⁡(96-digit number)
47018299021250020621…40071142318913297921
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
9.403 Γ— 10⁹⁡(96-digit number)
94036598042500041243…80142284637826595839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.403 Γ— 10⁹⁡(96-digit number)
94036598042500041243…80142284637826595841
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
1.880 Γ— 10⁹⁢(97-digit number)
18807319608500008248…60284569275653191679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.880 Γ— 10⁹⁢(97-digit number)
18807319608500008248…60284569275653191681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.761 Γ— 10⁹⁢(97-digit number)
37614639217000016497…20569138551306383359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,981,945 XPMΒ·at block #6,842,193 Β· updates every 60s
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