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Block #1,618,478

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/7/2016, 9:39:28 PM Β· Difficulty 10.5879 Β· 5,197,869 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
82bff873fbc681cb112d1eb55b5280459b2d128cdb199f648649c84264c61b3f
View on Chainz β†—

Height

#1,618,478

Difficulty

10.587877

Transactions

2

Size

14.00 KB

Version

2

Bits

0a967f1c

Nonce

1,133,750,116

Timestamp

6/7/2016, 9:39:28 PM

Confirmations

5,197,869

Mined by

⛏️ P2SHAMn3EopqHUbNdpp4Yi5wdpryieLB7CjyZ9

Merkle Root

e00c2bc644354a9b6f2ef947f20cbc458f63ac021907bb34a3c9751ac949b9b9
Transactions (2)
Coinbase50be6105613385…34bd94179830c0
1 in β†’ 1 out9.0700 XPM109 B
AMn3Eopq…LB7CjyZ9
cb6d71042fa8cc…6737bf1a113765
95 in β†’ 2 out46.1397 XPM13.80 KB
AV2V1Fp8…jkkNUxTVAbbBC9Dj…paytV5n1
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.

1.697 Γ— 10⁹⁴(95-digit number)
16976275907260050421…29110881636866621439
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
1.697 Γ— 10⁹⁴(95-digit number)
16976275907260050421…29110881636866621439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.697 Γ— 10⁹⁴(95-digit number)
16976275907260050421…29110881636866621441
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
3.395 Γ— 10⁹⁴(95-digit number)
33952551814520100843…58221763273733242879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.395 Γ— 10⁹⁴(95-digit number)
33952551814520100843…58221763273733242881
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
6.790 Γ— 10⁹⁴(95-digit number)
67905103629040201687…16443526547466485759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.790 Γ— 10⁹⁴(95-digit number)
67905103629040201687…16443526547466485761
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
1.358 Γ— 10⁹⁡(96-digit number)
13581020725808040337…32887053094932971519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.358 Γ— 10⁹⁡(96-digit number)
13581020725808040337…32887053094932971521
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
2.716 Γ— 10⁹⁡(96-digit number)
27162041451616080674…65774106189865943039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.716 Γ— 10⁹⁡(96-digit number)
27162041451616080674…65774106189865943041
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:57,774,900 XPMΒ·at block #6,816,346 Β· updates every 60s
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