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Block #1,746,772

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/3/2016, 7:06:42 PM Β· Difficulty 10.7123 Β· 5,086,438 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
df0d5beb98b5038adee0707920ac8a833a934f3dbf3eeefc0d98c57ba4e5e31a
View on Chainz β†—

Height

#1,746,772

Difficulty

10.712278

Transactions

1

Size

244 B

Version

2

Bits

0ab657db

Nonce

870,600,727

Timestamp

9/3/2016, 7:06:42 PM

Confirmations

5,086,438

Mined by

⛏️ P2SHAWCZr1QBXVx2mgQieugvyBQxKC7HWVxGPo

Merkle Root

ca5f9bcf6d75bf2f6a9994841f4554c07bf1335cf28cceaebb5401af7a7cad80
Transactions (1)
Coinbaseca5f9bcf6d75bf…5401af7a7cad80
1 in β†’ 2 out8.7000 XPM152 B
AWCZr1QB…7HWVxGPoALPu3s2c…EJXLjVFh
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.

4.808 Γ— 10⁹⁸(99-digit number)
48087991769326045033…28318807779071590399
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
4.808 Γ— 10⁹⁸(99-digit number)
48087991769326045033…28318807779071590399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.808 Γ— 10⁹⁸(99-digit number)
48087991769326045033…28318807779071590401
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
9.617 Γ— 10⁹⁸(99-digit number)
96175983538652090066…56637615558143180799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.617 Γ— 10⁹⁸(99-digit number)
96175983538652090066…56637615558143180801
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
1.923 Γ— 10⁹⁹(100-digit number)
19235196707730418013…13275231116286361599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.923 Γ— 10⁹⁹(100-digit number)
19235196707730418013…13275231116286361601
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
3.847 Γ— 10⁹⁹(100-digit number)
38470393415460836026…26550462232572723199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.847 Γ— 10⁹⁹(100-digit number)
38470393415460836026…26550462232572723201
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
7.694 Γ— 10⁹⁹(100-digit number)
76940786830921672053…53100924465145446399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.694 Γ— 10⁹⁹(100-digit number)
76940786830921672053…53100924465145446401
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:57,909,865 XPMΒ·at block #6,833,209 Β· updates every 60s
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